Multiple Holomorphs of Dihedral and Quaternionic Groups
نویسنده
چکیده
The holomorph of a group G is NormB(λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We explore the multiple holomorphs of the dihedral groups Dn and quaternionic (dicyclic) groups Qn for n ≥ 3.
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