منابع مشابه
Homology of Holomorphs of Free Groups
The holomorph of a free group Fn is the semidirect product FnoAut(Fn). Using the methods of Hatcher and Vogtmann in [10] and [11], we derive stability results and calculate the mod-p homology of these holomorphs for odd primes p in dimensions 1 and 2, and their rational homology in dimensions 1 through 5. Calculations of the twisted (where Aut(Fn) acts by first projecting to Gln(Z) and then inc...
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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...
متن کاملSome Observations regarding the Holomorphs of Finite Abelian Groups
Presentations for the holomorphs of abelian groups of the form Cpn × 1 for p=2 or an odd prime are given. These presentations extend the results given in Burnside’s well-known text on finite groups on the holomorphs for the cyclic groups of orders p for p being an odd or even prime. The following set of observations all deal with the holomorphs of finite abelian groups. The motivation here is t...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1961
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1961.11.1443