CLASS LENGTH OF ELEMENTS OF GROUP IN THE NORMALIZED UNIT GROUP

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International Electronic Journal of Algebra
Volume:26 Issue:26
CLASS LENGTH OF ELEMENTS OF GROUP IN THE NORMALIZED UNIT GROUP

CLASS LENGTH OF ELEMENTS OF GROUP IN THE NORMALIZED UNIT GROUP

Authors : Surinder KAUR, Manju KHAN

Pages : 41-52

Doi:10.24330/ieja.586920

View : 14 | Download : 10

Publication Date : 2019-07-11

Article Type : Research Paper

Abstract :Let F be a finite fi eld of characteristic p > 0. In this article, we obtain a relation between the class length of elements of a fi nite p-group G in the normalized unit group Vinsert ignore into journalissuearticles values(FG); and its unitary subgroup V*insert ignore into journalissuearticles values(FG);, when p is an odd prime. We also provide the size of the conjugacy class of non-central elements of a group G in Vinsert ignore into journalissuearticles values(FG);; where either G is any finite p-group with nilpotency class 2 or G is a p-group with nilpotency class 3 such that |G|<= p^5.
Keywords : Group ring, unit group, unitary units, conjugacy class

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