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A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g 2, ... , g n−1}, where e is the identity element and g i = g j whenever i ≡ j (mod n); in particular g n = g 0 = e, and g −1 = g n−1.
Also, members of older groups tended to perceive their groups to have more of the characteristics of Stage-3 and Stage-4 groups and to be more productive. Based on these results, Wheelan's position supports the traditional linear models of group development and casts doubt on the cyclic models and Gersick's punctuated equilibrium model.
cyclic group A cyclic group is a group that is generated by a single element, that is, a group such that there is an element g in the group such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse.
Now from the fact that in a group if ab = e then ba = e, it follows that any cyclic permutation of the components of an element of X again gives an element of X. Therefore one can define an action of the cyclic group C p of order p on X by cyclic permutations of components, in other words in which a chosen generator of C p sends
A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for example, a single p-adic analytic group G has a family of quotients which are finite p-groups of various orders, and properties of G translate into the properties of its finite quotients.
Group dynamics is a system of behaviors and psychological processes occurring within a social group (intragroup dynamics), or between social groups (intergroup dynamics). The study of group dynamics can be useful in understanding decision-making behaviour, tracking the spread of diseases in society, creating effective therapy techniques, and ...
Graves used a variety of names for his theory during his lifetime, ranging from the generic Levels of Human Existence in his earlier work [5] to lengthy names such as Emergent Cyclical, Phenomenological, Existential Double-Helix Levels of Existence Conception of Adult Human Behavior (1978) and Emergent Cyclical Double-Helix Model of the Adult Bio-Pyscho-Social Behaviour (1981).
The lattice of subgroups of the infinite cyclic group can be described in the same way, as the dual of the divisibility lattice of all positive integers. If the infinite cyclic group is represented as the additive group on the integers, then the subgroup generated by d is a subgroup of the subgroup generated by e if and only if e is a divisor ...