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Paper   IPM / M / 17163
School of Mathematics
  Title:   Extending Camina pairs
  Author(s):  Zeinab Aghajani (Joint with A. Beltran)
  Status:   Published
  Journal: J. Algebra
  Vol.:  662
  Year:  2023
  Pages:   220-232
  Supported by:  IPM
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 ∈ G − N and n ∈ 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 g−1 for all g ∈ G − N and all n ∈ N

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