On the index of a free abelian subgroup in the group of central units of an integral group ring

被引:3
|
作者
Bakshi, Gurmeet K. [1 ]
Maheshwary, Sugandha [1 ]
机构
[1] Panjab Univ, Ctr Adv Study Math, Chandigarh 160014, India
关键词
Integral group rings; Unit group; Central units; Generalized Bass units; Wedderburn decomposition; Strong Shoda pairs; Strongly monomial groups; Normally monomial groups;
D O I
10.1016/j.jalgebra.2015.03.012
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let Z(u(Z[G])) denote the group of central units in the integral group ring Z[G] of a finite group G. A bound on the index of the subgroup generated by a virtual basis in Z(u(Z[G])) is computed for a class of strongly monomial groups. The result is illustrated with application to the groups of order p(n), p prime, n <= 4. The rank of Z(u(Z[G])) and the Wedderburn decomposition of the rational group algebra of these p-groups have also been obtained. (C) 2015 Elsevier Inc. All rights reserved.
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页码:72 / 89
页数:18
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