Boundedly generated subgroups of finite groups
-
Andrea Lucchini
,
Marta Morigi
Abstract.
The starting point for this work was the question whether every finite group G contains a two-generated subgroup H such that 
, where 
denotes the set of primes dividing the order of G. We answer the question in the affirmative and address the following more general problem.
Let G be a finite group and let 
be a property of G. What is the minimum number t such that G contains a t-generated subgroup H satisfying the condition that 
? In particular, we consider the situation where is the set of composition factors (up to isomorphism), the exponent, the prime graph, or the spectrum of the group G. We give a complete answer in the cases where is the prime graph or the spectrum (obtaining that 
in the former case and t can be arbitrarily large in the latter case). We also prove that if is the exponent of G, then t is at most four.
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Representations of quivers over a ring and the Weak Krull–Schmidt Theorems
- Logarithmically improved regularity criteria for the 3D viscous MHD equations
- Tilting modules and universal localization
- A bound on the degree of schemes defined by quadratic equations
- Hardy's inequality in the scope of Dirichlet forms
- On some Banach spaces of martingales associated with function spaces
- Construction of quasi-periodic response solutions in forced strongly dissipative systems
- On the description of Leibniz superalgebras of nilindex
- Presentations of graph braid groups
- On the vanishing of the lower K-theory of the holomorph of a free group on two generators
- Boundedly generated subgroups of finite groups
