39,083 research outputs found
Computing generators of the unit group of an integral abelian group ring
We describe an algorithm for obtaining generators of the unit group of the
integral group ring ZG of a finite abelian group G. We used our implementation
in Magma of this algorithm to compute the unit groups of ZG for G of order up
to 110. In particular for those cases we obtained the index of the group of
Hoechsmann units in the full unit group. At the end of the paper we describe an
algorithm for the more general problem of finding generators of an arithmetic
group corresponding to a diagonalizable algebraic group
The mod 2 cohomology of the infinite families of Coxeter groups of type B and D as almost Hopf rings
We describe a Hopf ring structure on the direct sum of the cohomology groups
of the Coxeter
groups of type , and an almost-Hopf ring structure on the direct sum of
the cohomology groups of the Coxeter groups of type , with coefficient in the field
with two elements . We give presentations with generators and
relations, determine additive bases and compute the Steenrod algebra action.
The generators are described both in terms of a geometric construction by De
Concini and Salvetti and in terms of their restriction to elementary abelian
2-subgroups.Comment: 32 page
- β¦