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On groups which are the product of abelian subgroups

Published online by Cambridge University Press:  18 May 2009

Bernhard Amberg
Bernhard Amberg
Affiliation:
Johannes Gutenberg-Uniyersität Mainz, D6500 MainzWest Germany
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If the group G=AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Itô [8], so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:

There exists a normal subgroup

which is contained in A or B.

Recently, Holt and Howlett in [7] have given an example of a countably infinite p-group G = AB, which is the product of two elementary abelian subgroups A and B with Core(A) = Core (B) = 1, so that in this group (*) does not hold. Also, Sysak in [13] gives an example of a product G = AB of two free abelian subgroups A and B with Core(A)=Core(B)=l.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 2 , July 1985 , pp. 151 - 156
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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