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Research Article

Nilpotent Covers of Small Symmetric and Alternating Groups

Authors

  • Kimeu Arphaxad Ngwava Department of Mathematics, Physics and Computing, Moi University
  • Fredrick Oluoch Nyamwala Department of Mathematics, Physics and Computing, Moi University
  • Nick Gill School of Mathematics and Statistics, The Open University, Milton
  • Ian Short School of Mathematics and Statistics, The Open University, Milton

Abstract

We compute the size of a minimal nilpotent cover for small alternating and symmetric groups, An and Sn. We give precise values for values of n up to 8. For n=9 we give upper and lower bounds for the size of a minimal nilpotent cover of  A9.

Article information

Journal

Journal of Mathematics and Statistics Studies

Volume (Issue)

6 (2)

Pages

20-24

Published

2025-05-16

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287

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697

Keywords:

Alternating group; nilpotent cover; symmetric group