Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897361 | Journal of Pure and Applied Algebra | 2018 | 21 Pages |
Abstract
Let p>3 be a prime. For each maximal subgroup H⩽GL(d,p) with |H|⩾p3d+1, we construct a d-generator finite p-group G with the property that Aut(G) induces H on the Frattini quotient G/Φ(G) and |G|⩽pd42. A significant feature of this construction is that |G| is very small compared to |H|, shedding new light upon a celebrated result of Bryant and Kovács. The groups G that we exhibit have exponent p, and of all such groups G with the desired action of H on G/Φ(G), the construction yields groups with smallest nilpotency class, and in most cases, the smallest order.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
John Bamberg, S.P. Glasby, Luke Morgan, Alice C. Niemeyer,