Vol. 110, No. 1, 1984

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Colorings of hypermaps and a conjecture of Brenner and Lyndon

Giuliana Bianchi and Robert Cori

Vol. 110 (1984), No. 1, 41–48
Abstract

In this paper the following result is obtained: Let α and β be two permutations such that αβ is transitive and αp = βq = 1 (where p and q are distinct primes). Then the set of all permutations commuting both with α and β is either reduced to the identity or one of the three cyclic groups Cp, Cq or Cpq.

Mathematical Subject Classification 2000
Primary: 20B05
Secondary: 05C75, 20F32
Milestones
Received: 9 December 1981
Revised: 24 May 1982
Published: 1 January 1984
Authors
Giuliana Bianchi
Robert Cori