# Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples

@article{Fawcett2016BaseSO,
title={Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples},
author={Joanna B. Fawcett and Cheryl E. Praeger},
journal={Archiv der Mathematik},
year={2016},
volume={106},
pages={305-314}
}
• Published 16 February 2016
• Mathematics
• Archiv der Mathematik
For a subgroup L of the symmetric group $${S_{\ell}}$$Sℓ, we determine the minimal base size of $${GL_d(q) \wr L}$$GLd(q)≀L acting on $${V_d(q)^{\ell}}$$Vd(q)ℓ as an imprimitive linear group. This is achieved by computing the number of orbits of GLd(q) on spanning m-tuples, which turns out to be the number of d-dimensional subspaces of Vm(q). We then use these results to prove that for certain families of subgroups L, the affine groups whose stabilisers are large subgroups of {GL_{d}(q) \wr L…
2 Citations

## References

SHOWING 1-10 OF 16 REFERENCES

• Mathematics
• 1998
Let G be a permutation group on a finite set Ω. A sequence B=(ω1, …, ωb) of points in Ω is called a base if its pointwise stabilizer in G is the identity. Bases are of fundamental importance in
• Mathematics
• 1984
Let G be a permutation group on a finite set f2 of size n. Then G acts naturally on the set P (f2) of all subsets of f2. In this note we shall show that if G is primitive on f2 and A, $G then in all • Mathematics • 2013 Let G be a permutation group on a finite set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A Abstract. Let G be a permutation group on a finite set$\Omega $. If G does not involve An for$n \geqq 5 $, then there exist two disjoint subsets of$\Omega \$ such that no Sylow subgroup of G
• Mathematics
• 1999
In recent years probabilistic methods have proved useful in the solution of several problems concerning finite groups, mainly involving simple groups and permutation groups. In some cases the
• Mathematics
• 1995
Adxd matrix X over a field F is said to be cyclic if its characteristic polynomial cx{t) is equal to its minimal polynomial mx(t). This condition guarantees that the vector space V:= F of 1 x d row
A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive