Affiliation:
1. Department of Mathematics, University of Allahabad, Allahabad 211 002, India
Abstract
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary proof of the main theorem of a paper of Lal and Shukla, which avoids the use of the classification of finite simple groups. Further, we study the isotopy between the transversals in some groups and determine the number of isotopy classes of transversals of a subgroup of order 2 in D2p, the dihedral group of order 2p, where p is an odd prime and the isotopism classes are formed with respect to induced right loop structures.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
3 articles.
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1. Classifying gyrotransversals in groups;Asian-European Journal of Mathematics;2021-02-26
2. Isomorphism classes of transversals in finite nilpotent groups;Communications in Algebra;2020-07-31
3. Isotopic Classes of Transversals in Dihedral Group D2n, n Odd;Proceedings of the National Academy of Sciences, India Section A: Physical Sciences;2019-08-05