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Multiple semidirect products of associative systems

Published online by Cambridge University Press:  18 May 2009

Richard Steiner
Richard Steiner
Affiliation:
Department of Mathematics, University of GlasgowUniversity of Gardens, Glasgow G12 8QW
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Suppose that a group G is the semidirect product of a subgroup N and a normal subgroup M. Then the elements of G have unique expressions mn (m ∈ M, n ∈ N) and the commutator function

maps N x M into M. In fact there is an action (by automorphisms) of N on M given by

Conversely, if one is given an action of a group N on a group M then one can construct a semidirect product.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 353 - 369
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

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