Colorings of hypermaps and a conjecture of Brenner and Lyndon

Giuliana Bianchi and Robert Cori

Vol. 110 (1984), No. 1, 41–48

DOI: 10.2140/pjm.1984.110.41

Abstract

In this paper the following result is obtained: Let α and β be two permutations such that αβ is transitive and α^p = β^q = 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 C_p, C_q or C_pq.

Mathematical Subject Classification 2000

Primary: 20B05

Secondary: 05C75, 20F32

Milestones

Received: 9 December 1981

Revised: 24 May 1982

Published: 1 January 1984