Algebra and Logic

, Volume 35, Issue 4, pp 236–240 | Cite as

The intersection of Sylow subgroups in finite groups

  • V. I. Zenkov
  • V. D. Mazurov
Article

Abstract

In Theorem 1, letting p be a prime, we prove: (1) If G=Sn is a symmetric group of degree n, then G contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 2), (2, 4), (2, 8)}, and (2) If H=An is an alternating group of degree n, then H contains two Sylow p-subgroups with trivial intersection iff (p, n) ∉ {(3, 3), (2, 4)}. In Theorem 2, we argue that if G is a finite simple non-Abelian group and p is a prime, then G contains a pair of Sylow p-subgroups with trivial intersection. Also we present the corollary which says that if P is a Sylow subgroup of a finite simple non-Abelian group G, then ‖G‖>‖P‖2.

Keywords

Mathematical Logic Finite Group Symmetric Group Sylow Subgroup Trivial Intersection 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. I. Zenkov
  • V. D. Mazurov

There are no affiliations available

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