Set-Theoretic Operations

Subsections

• Membership and Equality

Membership and Equality

g in A : GrpAbGenElt, GrpAbGen -> BoolElt

Given an element g and a group A, return true if g is an element of A, false otherwise.

g notin A : GrpAbGenElt, GrpAbGen -> BoolElt

Given an element g and a group A, return true if g is not an element of A, false otherwise.

S subset A : { GrpAbGenElt } , GrpAbGen -> BoolElt

Given an group A and a set S of elements belonging to a group H, where A and H have some covering group, return true if S is a subset of A, false otherwise.

S notsubset A : { GrpAbGenElt } , GrpAbGen -> BoolElt

Given a group A and a set S of elements belonging to a group H, where A and H have some covering group, return true if S is not a subset of G, false otherwise.

H subset A : GrpAbGen, GrpAbGen -> BoolElt

Given groups A and H, subgroups of some common overgroup, return true if H is a subgroup of A, and false otherwise.

H notsubset A : GrpAbGen, GrpAbGen -> BoolElt

Given groups A and H, subgroups of some common overgroup, return true if H is not a subgroup of A, and false otherwise.

A eq B : GrpAbGen, GrpAbGen -> BoolElt

Given groups A and B, subgroups of some common overgroup, return true if A and B are identical, and false otherwise.

A ne B : GrpAbGen, GrpAbGen -> BoolElt

Given groups A and B, subgroups of some common overgroup, return true if A and B are distinct groups, and false otherwise.