Group Axioms

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Group (mathematics) - In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. For example, the set of integers is a group under the operation of addition.

Archimedean group - In abstract algebra, a branch of mathematics, an Archimedean group is an algebraic structure. It is a set together with a binary operation and binary relation, with both satisfying certain axioms detailed below.

Primary group/Secondary group - A Primary group is a typically small social group whose members share close, personal, enduring Primary relationships. These groups are marked by member's concern for one another, shared activities and culture, and long periods of time spent together.

Permutation group - In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself); the relationship is often written as (G,M). Note that the group of all permutations of a set is the symmetric group; the term permutation group is usually restricted to mean a subgroup of the symmetric group.

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