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On a problem of P. Hall about groups isomorphic to all their non-trivial normal subgroups

Published online by Cambridge University Press:  01 July 1997

VN Obraztsov
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Abstract

A scheme of construction of infinite groups, other than simple groups, free groups of infinite rank and the infinite cyclic group, which are isomorphic to all their non-trivial normal subgroups is presented. Some results about the automorphism groups of simple infinite groups are also obtained. In particular, it is proved that there is an infinite group $G$ of any sufficiently large prime exponent $p$ (or which is torsion-free) all of whose proper subgroups are cyclic, and such that the groups ${\rm Aut}\,G$ and ${\rm Out}\,G$ are isomorphic. The proofs use the technique of graded diagrams developed by A. Yu. Ol'shanskii.

1991 Mathematics Subject Classification: 20F05, 20F06.

Keywords

normal subgroupautomorphism groupgraded diagram
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 1 , July 1997 , pp. 79 - 98
Copyright
London Mathematical Society 1997

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