ITÔ’S THEOREM ON GROUPS WITH TWO CLASS SIZES REVISITED.

Authors

  • Elena Alemany
  • Antonio Beltrán
  • Maria José Felipe

Keywords:

Finite groups, conjugacy class sizes, solvable groups.

Abstract

Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p^aq^b, for two distinct primes p and q, and G either has abelian p-complement or G = PQ × A, with P and Q a Sylow p-subgroup and a Sylow q-subgroup of G, respectively. In particular, we provide a new extension of Itô’s Theorem on groups having exactly two class sizes for elements of prime power order. DOI: 10.1017/S0004972711002875

Published

2012-04-22

Issue

Vol. 85 No. 3 (2012)

Section

Articles
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