“School of Mathematics”
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| Paper IPM / M / 17163 |
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| Abstract: | |
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et G be a finite group and N a nontrivial proper normal
subgroup of G. A.R. Camina introduced the class of finite
groups G, which extends Frobenius groups, satisfying that for
all g â G â N and n â N, gn is conjugate to g. He proved
that under these assumptions one of three possibilities occurs:
G is a Frobenius group with kernel N; or N is a p-group;
or G/N is a p-group. In this paper we extend this class of
groups by investigating the structure of those finite groups G
having a nontrivial proper normal subgroup N such that gn is
conjugate to either g or gâ1 for all g â G â N and all n â N
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