CLASS LENGTH OF ELEMENTS OF GROUP IN THE NORMALIZED UNIT GROUP

Yıl 2019, Cilt: 26 Sayı: 26, 41 - 52, 11.07.2019

Surinder Kaur Manju Khan

https://doi.org/10.24330/ieja.586920

Öz

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 V(FG) and its unitary subgroup V*(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 V(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.

Anahtar Kelimeler

Group ring, unit group, unitary units, conjugacy class

Kaynakça

• A. A. Bovdi and I. I. Hripta, Normal subgroups of the multiplicative group of a ring, Mat. Sb. (N.S.), 87(129) (1972), 338-350.
• A. A. Bovdi and S. V. Mihovski, Conjugacy classes in group algebras of p-groups, C. R. Acad. Bulgare Sci., 56(1) (2003), 5-8.
• A. A. Bovdi and C. Polcino Milies, Conjugacy classes of the group of units in group algebras of finite p-groups, Euroconference on Algebra and Represen- tation Theory (Constantza, 2000), An. Stiint. Univ. Ovidius Constanta Ser. Mat., 8(2) (2000), 1-12.
• V. Bovdi and A. L. Rosa, On the order of the unitary subgroup of a modular group algebra, Comm. Algebra, 28(4) (2000), 1897-1905.
• A. Bovdi, L. G. Kovacs and S. Mihovski, On the orders of conjugacy classes in group algebras of p-groups, J. Aust. Math. Soc., 77(2) (2004), 185-189.
• D. B. Coleman, On the modular group ring of a p-group, Proc. Amer. Math. Soc., 15 (1964), 511{514.
• M. A. Rao and R. Sandling, Vanishing orbit sums in group algebras of p-groups, Groups '93 Galway/St. Andrews, Vol. 2, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 212 (1995), 507-511.