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Abstract
Let p>3 be a prime. For each maximal subgroup H⩽GL(d,p) with H⩾p^{3d+1}, we construct a dgenerator finite pgroup G with the property that Aut(G) induces H on the Frattini quotient G/Φ(G) and G⩽p^{[Formula presented]}. 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.
Original language  English 

Pages (fromto)  29312951 
Number of pages  21 
Journal  Journal of Pure and Applied Algebra 
Volume  222 
Issue number  10 
DOIs  
Publication status  Published  1 Oct 2018 
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Dive into the research topics of 'Maximal linear groups induced on the Frattini quotient of a pgroup'. Together they form a unique fingerprint.Projects
 4 Finished

Structure theory for permutation groups and local graph theory conjectures
1/01/16 → 31/01/19
Project: Research

Finite linearly representable geometries and symmetry
Praeger, C., Glasby, S. & Niemeyer, A.
1/01/14 → 31/05/19
Project: Research
