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On F-groups with the central factor of order p4

  • Seyyed Majid Jafarian Amiri EMAIL logo , Halimeh Madadi and Hojjat Rostami
Published/Copyright: September 22, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 5

Abstract

A finite group G is called an F-group (G ∈ F) if for every x, y ∈ G ∖ Z(G), CG(x) ≤ CG(y) implies that CG(x) = CG(y). An important subclass of F-groups are CA-groups, consisting of groups in which all centralizers of noncentral elements are abelian. In this paper, among other results, we find the number of element centralizers and the maximum cardinality of subsets of pairwise non-commuting elements in an F-group G with |GZ(G)| = p4 for some prime p.

MSC 2010: 20D15
Keywords: p-group; F-group; non-commuting element; centralizer

(Communicated by Vincenzo Marra)

Acknowledgement

The authors thank the anonymous referee for his/her useful comments and suggestions which substantially improved the paper.

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Received: 2015-11-19
Accepted: 2015-12-1
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0038
Keywords for this article
p-group; F-group; non-commuting element; centralizer

Articles in the same Issue

  2. Cyclic and rotational latin hybrid triple systems
  4. Notes on mildly distributive semilattices
  6. On generalized completely distributive posets
  8. Properties of non-associative MV-algebras
  10. On the upper and lower exponential density functions
  12. Quadratic permutations, complete mappings and mutually orthogonal latin squares
  14. On F-groups with the central factor of order p4
  16. Comparison of some families of real functions in porosity terms
  18. Negative interest rates: why and how?
  20. Homoclinic and heteroclinic motions in hybrid systems with impacts
  22. Some fixed point theorems in Branciari metric spaces
  24. S-essential spectra and measure of noncompactness
  26. Unified approach to graphs and metric spaces
  28. On structural properties of porouscontinuous functions
  30. A class of topological spaces between the classes of regular and urysohn spaces
  32. On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
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