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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, g2, ... , gn−1}, where e is the identity element and gi = gj whenever i ≡ j (mod n); in particular gn = g0 = e, and g−1 = gn−1.
Group development. The goal of most research on group development is to learn why and how small groups change over time. To quality of the output produced by a group, the type and frequency of its activities, its cohesiveness, the existence of group conflict. A number of theoretical models have been developed to explain how certain groups ...
Cyclic order. The months are a cyclic order. In mathematics, a cyclic order is a way to arrange a set of objects in a circle. [nb] Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as " a < b ". One does not say that east is "more clockwise" than west. Instead, a cyclic order is defined as a ...
t. e. Circular reasoning (Latin: circulus in probando, "circle in proving"; [1] also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. [2] Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of ...
In group theory, a dicyclic group (notation Dicn or Q4n, [1] n,2,2 [2]) is a particular kind of non-abelian group of order 4 n (n > 1). It is an extension of the cyclic group of order 2 by a cyclic group of order 2 n, giving the name di-cyclic. In the notation of exact sequences of groups, this extension can be expressed as:
The subgroup of order n / d is a subgroup of the subgroup of order n / e if and only if e is a divisor of d. 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 ...
In mathematics, a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order. Cyclically ordered groups were first studied in depth by Ladislav Rieger in 1947. [1] They are a generalization of cyclic groups: the infinite cyclic group Z and the finite ...
The principles of grouping (or Gestalt laws of grouping) are a set of principles in psychology, first proposed by Gestalt psychologists to account for the observation that humans naturally perceive objects as organized patterns and objects, a principle known as Prägnanz. Gestalt psychologists argued that these principles exist because the mind ...