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Bulletin of the London Mathematical Society Advance Access originally published online on April 23, 2008
Bulletin of the London Mathematical Society 2008 40(3):415-431; doi:10.1112/blms/bdn021
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© 2008 London Mathematical Society

Higman's PORC conjecture for a family of groups

Anton Evseev

Selwyn College
Cambridge
CB3 9DQ
United Kingdom

Received 15 July 2007. Revision received 12 December 2007.

We prove that the number of groups of order pn with central Frattini subgroup is, for fixed n, a PORC (‘polynomial on residue classes’) function of the prime p. This extends a result of Higman.

2000 Mathematics Subject Classification 20D15 (primary), 20J05 (secondary).


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