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Paper   IPM / M / 765
School of Mathematics
  Title:   On the number of maximal theta pairs in a finite group
  Author(s):  A. R. Ashrafi
  Status:   Published
  Journal: Acta Math. Inform. Univ. Ostraviensis
  Vol.:  9
  Year:  2001
  Pages:   5-12
  Supported by:  IPM
  Abstract:
In [6], Bhattacharya and Mukherjee defined the notion of θ-pair for a maximal subgroup of a finite group. They proved that for any maximal subgroup M of a finite group G, there exists a θ-pair related to M. In [11], Zhao improved this result. He proved that for any maximal subgroup M of a finite group G, there exists a normal maximal θ-pair related to M. In this paper we introduce the notion of nθ-maximal and primitive nθ-maximal group. We show that for n=1,2,G is nθ-maximal if and only if G is primitive nθ-maximal. Also, we characterize the 1θ-maximal group and prove some results about 2θ-maximal groups. Finally, we introduce the notion of nθ-pair group and prove that for all n ≠ 2,3, there exists nθ-pair groups and for n=2,3 there is no nθ-pair groups.

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