Bhandari, Ashwani K. ; Luthar, Indar S.
(1984)
*Certain conjugacy classes of units in integral group rings of metacyclic groups*
Journal of Number Theory, 18
(2).
pp. 215-228.
ISSN 0022-314X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002231...

Related URL: http://dx.doi.org/10.1016/0022-314X(84)90056-8

## Abstract

Let G be the metacyclic group of order pq given by G = <σ, τ: σ^{p} = 1 = τ^{q}, τστ^{-} = σ^{j}> where p is an odd prime, q ≥ 2 a divisor of p - 1, and where j belongs to the exponent q mod p. Let V denote the group of units of augmentation 1 in the integral group ring Z G of G. In this paper it is proved that the number of conjugacy classes of elements of order p in V is (p - 1)^{q-1} μ_{0} H/vq where ν, μ_{0}, and H are suitably defined numbers.

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Deposited On: | 23 Dec 2010 03:53 |

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