In this paper we prove that if G is a group which is the union of the conjugates of a finite subgroup H , then we have G = H if H= PSL(2,2^n ), n ∈ N \ {0} or H is a generalized dihedral group. This result extends Theorem 3 of Cutolo et al. (2005) [1] proved only in the case H PSL(2,4).
A note on groups covered by conjugates of a proper subgroup.
JABARA, Enrico
2012-01-01
Abstract
In this paper we prove that if G is a group which is the union of the conjugates of a finite subgroup H , then we have G = H if H= PSL(2,2^n ), n ∈ N \ {0} or H is a generalized dihedral group. This result extends Theorem 3 of Cutolo et al. (2005) [1] proved only in the case H PSL(2,4).
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