Coset Spaces

Contents

Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
RightTransversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Given a group G and a subgroup H of G, this function returns:
(a)
An indexed set of elements T of G forming a right transversal for G over H; and,
(b)
The corresponding transversal mapping φ: G -> T. If T = { t1, ..., tr } and g in G, φ is defined by φ(g) = ti, where g∈H ti.

Coercions Between Groups and Subgroups

G ! g : GrpAb, GrpAbElt -> GrpAbElt
Given an element g belonging to the subgroup H of the group G, rewrite g as an element of G.
H ! g : GrpAb, GrpAbElt -> GrpAbElt
Given an element g belonging to the group G, and given a subgroup H of G containing g, rewrite g as an element of H.
K ! g : GrpAb, GrpAbElt -> GrpAbElt
Given an element g belonging to the group H, and a group K, such that H and K are subgroups of G, and both H and K contain g, rewrite g as an element of K.
Morphism(H, G) : GrpAb, GrpAb -> ModMatRngElt
The integer matrix defining the inclusion monomorphism from the subgroup H of G into G.
V2.28, 13 July 2023