Application of transfer maps on Factor Groups
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Date
1999-11-20
Authors
Seneviratne, P. S. B.
Journal Title
Journal ISSN
Volume Title
Publisher
Unviersity of Peradeniya, Peradeniya, Sri Lanka
Abstract
We wish to present the proofs of the following two results on transfer maps.
(i) Let G be a finite group and let K be a normal subgroup of order n of G such that G/K is abelian. If G splits over K with H as a complement to K, 𝜏 is the transfer of G into H, ψ is the map from G to H such that ψ(hk) = h, for all h in H, and k in K, and v is the map defined by v(h) = hⁿ, then 𝜏 = ψV.
(ii) Let G be a finite group. If G has an abelian Sylow p-subgroup then p does not divide |G'∩Z(G)|. Hence we show that if all Sylow p-subgroups of G are abelian then G'∩Z(G) = 1. Also, if G/Z(G) is a π group, then G' is also a π group. However, the converse of this result is not true. A counter example will be presented.
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Keywords
Technology , Engineering , Physical Sciences
Citation
Proceedings & abstracts of the Annual Research Sessions 1999, Unviersity of Peradeniya, Peradeniya, Sri Lanka, pp.104