7.101 SemidirectProduct for Groups

The function GroupOps.SemidirectProduct constructs the semidirect product as a group of semidirect product elements. In the following let G, a, and H be the arguments of SemidirectProduct.

Each such element (g,h) is represented by a record with the following components.

element:

the list [ g, h ].

automorphism:

contains the image of g under a.

isGroupElement:

always true.

isSemidirectProductElement:

always true.

domain:

contains GroupElements.

operations:

contains the operations record SemidirectProductOps.

The operations of semidirect product elements in done in the obvious way.

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