7.45 Properties and Property Tests

The following sections describe the functions that computes or test properties of groups (see AbelianInvariants, DimensionsLoewyFactors, EulerianFunction, Exponent, Factorization, Index, IsAbelian, IsCentral, IsConjugate, IsCyclic, IsElementaryAbelian, IsNilpotent, IsNormal, IsPerfect, IsSimple, IsSolvable, IsSubgroup, IsSubnormal, IsTrivial for Groups, GroupId, PermutationCharacter).

All tests expect a parent group or subgroup and return true if the group has the property and false otherwise. Some functions may not terminate if the given group has an infinite set of elements. A warning may be printed in such cases.

In addition the set theoretic functions Elements, Size and IsFinite, which are described in chapter Domains, can be used for groups. Size (see Size) returns the order of a group, this is either a positive integer or the string ``infinity''. IsFinite (see IsFinite) returns true if a group is finite and false otherwise.

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