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p. 664. Structure of groupslocked

  • Ian Stewart

Abstract

‘Structure of groups’ discusses the basic concepts of group theory. Isomorphism occurs when two technically distinct groups share the same abstract structure and order. Groups may also contain smaller subgroups — the orders of subgroups are divisions of the order of the whole group. Two symmetries of some objects may be essentially the same, but applied at different locations — a phenomenon known as conjugacy. A conjugacy class is a set of all elements conjugate to a given element. Quotient groups are a special kind of partition of a group, which can give rise to homomorphisms (which is related to isomorphisms), and normal groups.

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