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A Class of infinite soluble groups with an A-group condition

Published online by Cambridge University Press:  18 May 2009

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
University of Glasgow, Department of Mathematics, University Gardens, Glasgow, Scotland G12 8QW
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Finite soluble groups in which all the Sylow subgroups are abelian were first investigated by Taunt [8] who referred to them as A-groups. Locally finite groups with the same property have been considered by Graddon [2]. By the use of Sylow theorems it is clear that every section (homomorphic image of a subgroup) of an A-group is also an A-group and hence every nilpotent section of an A-group is abelian. This is the characterization that we use here in considering groups which are not, in general, periodic.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 81 - 84
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

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