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A Note On Transversals

Abstract

Let GG be a finite group and HH a core-free subgroup of GG. We will show that if there exists a solvable, generating transversal of HH in GG, then GG is a solvable group. Further, if SS is a generating transversal of HH in GG and SS has order 2 invariant sub right loop TT such that the quotient S/TS/T is a group. Then HH is an elementary abelian 2-group.Comment: 7 page

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