Central units of integral group rings of monomial groups

@inproceedings{Bakshi2022CentralUO,
  title={Central units of integral group rings of monomial groups},
  author={Gurmeet K. Bakshi and Gurleen Kaur},
  year={2022}
}
In this paper, it is proved that the group generated by Bass units contains a subgroup of finite index in the group of central units Z(U(ZG)) of the integral group ring ZG for a subgroup closed monomial group G with the property that every cyclic subgroup of order not a divisor of 4 or 6 is subnormal in G. If G is a generalized strongly monomial group, then it is shown that the group generated by generalized Bass units contains a subgroup of finite index in Z(U(ZG)). Furthermore, for a… 

A computational approach to Brauer Witt theorem using Shoda pair theory

A classical theorem due to Brauer and Witt implies that every simple component of the rational group algebra Q G of a finite group G is Brauer equivalent to a cyclotomic algebra containing Q in its

References

SHOWING 1-10 OF 26 REFERENCES

Central units of integral group rings of nilpotent groups

In this paper a finite set of generators is given for a subgroup of finite index in the group of central units of the integral group ring of a finitely generated nilpotent group. In this paper we

Structure of group rings and the group of units of integral group rings: an invitation

  • E. Jespers
  • Mathematics
    Indian Journal of Pure and Applied Mathematics
  • 2021
During the past three decades fundamental progress has been made on constructing large torsion-free subgroups (i.e. subgroups of finite index) of the unit group $\U (\Z G)$ of the integral group ring

Simple components and central units in group algebras

Central Units in Metacyclic Integral Group Rings

In this article, we give a method to compute the rank of the subgroup of central units of ℤ G, for a finite metacyclic group, G, by means of ℚ-classes and ℝ-classes. Then we construct a

On Monomial Characters and Central Idempotents of Rational Group Algebras

Abstract We give a method to obtain the primitive central idempotent of the rational group algebra ℚG over a finite group G associated to a monomial irreducible character which does not involve

Orders and Generic Constructions of Units

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of

The Units of Group‐Rings

when addition and multiplication are defined in the obvious way, form a ring, the group-ring of G over K, which will be denoted by R (G, K). Henceforward, we suppose that K has the modulus 1, and we