“School of Mathematics”
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Paper IPM / M / 17163  


Abstract:  
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 pgroup;
or G/N is a pgroup. 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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