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Cog's ladder of group development is based on the work, "Cog's Ladder: A Model of Group Growth", by George O. Charrier, an employee of Procter and Gamble, published in a company newsletter in 1972. The original document was written to help group managers at Procter and Gamble better understand the dynamics of group work, thus improving efficiency.
If a set is such that it cannot be endowed with a group structure, then it is necessarily non-wellorderable. Otherwise the construction in the second section does yield a group structure. However these properties are not equivalent. Namely, it is possible for sets which cannot be well-ordered to have a group structure.
Conflict is an inevitable part of this process. The group's task at Stage 2 is to develop a unified set of goals, values, and operational procedures, and this task inevitably generates some conflict. Conflict also is necessary for the establishment of trust and a climate in which members feel free to disagree with each other.
Initiating structure is the extent to which a leader defines leader and group member roles, initiates actions, organizes group activities and defines how tasks are to be accomplished by the group. This leadership style is task-oriented. Some of the statements used to measure this factor in the LBDQ are:
The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
If the algebraic group is the multiplicative group mod N, the one-sided identities are recognised by computing greatest common divisors with N, and the result is the p − 1 method. If the algebraic group is the multiplicative group of a quadratic extension of N, the result is the p + 1 method; the calculation involves pairs of numbers modulo N.
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In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field.
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