Hurwitz Groups with Given Centre | Zendy

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Hurwitz Groups with Given Centre

Author(s) -

Conder Marston

Publication year - 2002

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609302001352

Subject(s) - mathematics , abelian group , group (periodic table) , prime (order theory) , finite group , combinatorics , cyclic group , prime power , integer (computer science) , mathematics subject classification , discrete mathematics , pure mathematics , computer science , chemistry , organic chemistry , programming language

A Hurwitz group is any non‐trivial finite group that can be (2,3,7)‐generated; that is, generated by elements x and y satisfying the relations x 2 = y 3 = ( xy ) 7 = 1. In this short paper a complete answer is given to a 1965 question by John Leech, showing that the centre of a Hurwitz group can be any given finite abelian group. The proof is based on a recent theorem of Lucchini, Tamburini and Wilson, which states that the special linear group SL n ( q ) is a Hurwitz group for every integer n ⩾ 287 and every prime‐power q . 2000 Mathematics Subject Classification 20F05 (primary); 57M05 (secondary).

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