Hurwitz Groups with Given Centre |
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Authors: | Conder Marston |
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Institution: | Department of Mathematics, University of Auckland Private Bag 92019, Auckland, New Zealand conder{at}math.auckland.ac.nz |
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Abstract: | A Hurwitz group is any non-trivial finite group that can be(2,3,7)-generated; that is, generated by elements x and y satisfyingthe relations x2 = y3 = (xy)7 = 1. In this short paper a completeanswer is given to a 1965 question by John Leech, showing thatthe centre of a Hurwitz group can be any given finite abeliangroup. The proof is based on a recent theorem of Lucchini, Tamburiniand Wilson, which states that the special linear group SLn(q)is a Hurwitz group for every integer n 287 and every prime-powerq. 2000 Mathematics Subject Classification 20F05 (primary);57M05 (secondary). |
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