Any social group, therefore, will have a specified basis of social interaction, though the nature and extent of this will vary greatly between groups. Social groups of various types can be seen as the building blocks from which other types and levels of social organization are built.
Groups are subdivided into systems; several groups constitute an eono-thema. There are five groups: the Archean. The theory of groups studies the properties of operations that occur most frequently in mathematics and its applications from the most general point of view examples of such operations are multiplication of numbers, addition of vectors, successive accomplishment of transformations, and so on.
The generality of the theory of groups, and thus its wide applicability, stems from the fact that the theory studies the properties of operations in their pure form, ignoring the nature of the particular operation as well as the nature of the elements operated on. At the same time, it must be stressed that the theory of groups is restricted to the study of operations that satisfy a number of properties that are part of the definition of a group see below.
One way of arriving at the concept of a group is to study the symmetries of geometric figures. There are eight different motions that map the square to itself. In the case of the circle Figure 1,b the number of such motions is infinite; each rotation of the circle about its center is a motion of the required type.
In the case of the figure represented in Figure 1, c the only motion that maps it to itself is the identity transformation, that is, the transformation which leaves each point of the figure fixed.
Figure 1. The set G of motions that map a figure to itself is a measure of its symmetry; the larger the set G the more symmetric the figure.
The set G of motions of a figure together with the composition defined on G is called the group of symmetries of the figure. The subset H of even numbers is itself a group under addition. We say that H is a subgroup of G. A group with this additional property is said to be commutative, or Abelian. For example. The concept of a group served in many respects as a model for the restructuring of algebra and, more generally, of mathematics that took place at the turn of the 20th century.
The sources of the concept of a group are evident in several disciplines, the most important of which is the theory of solvability of algebraic equations by radicals.
In the French mathematicians J. Lagrange and A. Ruffini published a number of papers in and later devoted to the demonstration of the unsolva-bility of the general quintic by radicals in which he made systematic use of the closure of permutations under multiplication and determined in essence the subgroups of the group of permutations on five symbols. The deep ties between properties of groups of permutations and properties of equations were demonstrated by the Norwegian mathematician N.
Abel and the French mathematician E. Galois A treatise on groups of permutations published in by the French mathematician C. Jordan played an important role in the sys-tematization and development of group theory.
A resolution of this problem came from investigations in the area of projective geometry concerned with the behavior of figures under various transformations. Gradually, interest in these studies shifted to the transformations themselves and to their classification. The German mathematician A. Kleinwhich used groups of transformation as the basis for the classification of geometries. Specifically, a geometry is defined by a group of transformations of space, and the only properties of figures that belong to the geometty in question are the properties invariant with respect to the transformations in this group.
The third source of the group concept is number theory. Already inL. In group-theoretical terms this amounts to decomposition of a group into cosets with respect to a subgroup. Gauss, in his Disquisitiones Arithmeticaestudied, among others, the cyclotomic equation and, in essence, determined the subgroups of its Galois group.
The German mathematician L.The C T Group is a global organisation that integrates research, strategy and communications tools to execute winning campaigns for corporate and political clients.
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TP Group Annual Report The T-group approach has been used effectively in business schools, executive education programs and other learning and development initiatives in order to develop more self-aware, emotionally intelligent and effective leaders.
The learning process will take place on multiple levels:. The role of the T-group facilitators is to help to apply the T-group methodology to your own leadership and personal goals. T-Group is an experiential practice of many of the leadership skills necessary for building high-performing teams of diverse individuals in complex environments. Without an agenda, structure, or fabricated role plays, T-Group participants practice and develop core skills and behaviors through real-time interaction and dynamics.
In T-group interactions, participants and facilitators provide rare, actionable information about how one comes across and impacts and influences others.
These interpersonal exchanges can be vulnerable and, at times, difficult. Developing resilience when interacting with others is an important part of the T-group experience: learning how to peel different layers of conversation will lead to a mutual desired outcome, and to strengthening the relationships. Business today is done in a global settings. Once established, this trust will enable the group to make effective decisions, and operate in a high performance mode.
Like for many thousands of GSB alumni, the experience remained one of the most impactful learning she had both personally and professionally. Having experienced its transformative potential, Agnes became a trained T-group facilitator at the GSB.
Over and over, she was amazed by the result of this experiential learning. With a desire to bring this innovative approach to business leaders across the globe, not just for Stanford MBA students, she started T-Group International, an organization that collaborates with other talented facilitators and leverages their collective experience and their individual diversity.
As an entrepreneur in her early career, Dikla learned the hard way about the importance of relationships and effective leadership. Like many entrepreneurs, she was passionate about her ambitions, but did not always remember how much she needed others to make the dream come true. Years after she sold her company, she encountered new challenges: as an international professional living in the U.
As she searched for tools and knowledge to overcome these barriers, she become an avid practitioner of the T-Group training group methodology, both as a participant and — since — a facilitator.
Today, her passion centers on how group work can empower individuals by providing an environment for feedback and learning across cultural, social, and demographic differences. Our flagship program is a 5-day condensed format of Interpersonal Dynamics that combines short lectures and activities based on the T-group methodology.
Contact us for a sample schedule. We also tailor shorter or longer programs for corporate clients based on their needs.This gritty drama follows unlikely tech entrepreneurs behind a brilliant idea, and a powerful FBI agent who can make or break those he comes in contact with -- not always for the right reasons.
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This is used in various environments such as encounter groups and human relations but the goals will vary.
The leader of the T-Group is an individual who ensures that the environment is safe and secure for participants being that they should feel comfortable coming to the group and expressing their feelings with others. The discussions during training are brought up by members of the group and leaders will encourage individual thinking throughout the sessions. Sensitivity training increases individuality and interpersonal communication.
This is a method that branched from psychotherapy and can be used toward many social problems to initiate trust and communication between members. Each group has its own goal and progress speed. The members who are attending the group will all benefit from self expression and interaction with others.
The goal of T-group is to initiate social interaction, individuality and confidence in expression. The leader does not decide upon the topic of conversation.
Since the members choose what is going to be talked about they will participate more and express feelings that pertain to the therapy matter. As sessions go on each member of the group will gain self awareness. They will learn from the other members who also express their feelings toward the subject matter. If controversy is present within the group this will only increase the social interaction and allow members to gain more self awareness.
T-Group or Sensitivity Training is used and offered by organizations as a way for people within a community to learn about each other and themselves for the purpose of acceptance and awareness. The subjects of these groups are going to vary — they can be of any matter as long as it is presented for progressive reasons. It is used when participants put themselves in the shoes of others so that they can learn how to relate to them and understand their belief system or way of doing things.
It may be used toward multicultural and gender sensitivity subjects. Regardless, each person within the group is participating so that they can have a deeper understanding of others and what they believe themselves. The sessions start by uncovering an interaction that tends to spark interest and emotions amongst a diverse group of people.
As a mechanism to reintegrate individuals the topic often pertains to an issue that separates them from each other. During the sessions the conductor of the group will only be present to ensure that the environment is safe and comfortable for the members. Once they are present the topic of discussion will be chosen by the members themselves.T-group is a present moment authentic relating practice.
It is first and foremost a practice, in the way that martial arts, meditation, and yoga are practices. The practice begins with a meditative-like awareness of the present moment in your body: emotions and sensations. Thoughts can be part of the present moment, but rather than articulate and go into the thought or story around the experience, we strive to stay in awareness, as in meditation. Then we add interpersonal interaction and a group field with others striving to do the same thing. As humans, we are naturally very responsive to each other.
T-Group is a space to explore our responses to others primarily feelings and sensationsas they are happening. Interaction is slowed down in service to deeper understanding and awareness of self in the context of a small group. We strive to stay present with ourselves, while we are relating to others in an authentic way. We share our experience, what we notice and open to how our sharing impacts others and the group field. This is the fundamental practice.
T-Group is a relational practice. It requires people who agree to sit together and share their experiences in real time.
Each session runs 45 minutes, and after the session each participant has the chance to discuss the experience for one minute. We agree to stay present and available for the impact our truth has on others in the group. Discovering how we impact others is one of the most insightful parts of the T-Group experience.
We agree not to defend, explain, or lash out, even when something we hear feels hurtful or unfair. Instead, we agree to reveal the feelings, sensations and emotions that underlie the impulse to react—in other words, the impact the other person is having on our experience.
We agree to the use of three hand signals as a way to communicate with participants non-verbally without interrupting the flow of conversation: Wiggling fingers: I resonate with what you are saying Closing thumb and fingertips, drawing down hand: You are speaking about something that happened more than 30 seconds ago.
Open palm: Reveal your motivations before asking another to reveal theirs. T-groups tend to encourage vulnerability, revealing hidden emotions, and deep contact with others. If something comes up that you are not ready for, it is important to maintain your own agency and insist on your safety. We typically meet every Sunday night for the standard practice. We also meet an additional night once every couple months for intro training. T-Group is typically held at the house of one of the community members.