Wreath Products, Sylow's Theorem and Fermat's Little Theorem

Authors

  • B. Sury Indian Statistical Institute

Keywords:

wreath products, Sylow's theorem

Abstract

The assertion that the number of

p-Sylow subgroups in a finite group is = 1 mod p, begs the natural question whether one may obtain the power a^p-1 (for any (a, p) = 1) as the number of p-Sylow subgroups in some group naturally. Indeed, it turns out to be so as we show below. The construction involves wreath products of groups. Using wreath products, a different generalization of Euler’s congruence (and, a fortiori, of Fermat’s little theorem) was obtained in [1].

Author Biography

  • B. Sury, Indian Statistical Institute

    Associate Professor

    Stat-Math Unit

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Published

2009-12-24

Issue

Section

Algebra

How to Cite

Wreath Products, Sylow’s Theorem and Fermat’s Little Theorem. (2009). European Journal of Pure and Applied Mathematics, 3(1), 13-15. https://www.ejpam.com/index.php/ejpam/article/view/308

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