Butler groups splitting over a base element
We characterize a particular kind of decomposition of a Butler group that is the general case for Butler B(1)-groups; and exhibit a decomposition of a B(2)-group which is not of that kind.
A transvection decomposition in GL(n,2)
An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.
On Butler -groups decomposing over two base elements
A -group is a sum of a finite number of torsionfree Abelian groups of rank , subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.
On direct sums of -groups – II
-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, , Comment. Math. Univ. Carolinae (1993), 587–591, the problem of direct sums of -groups was discussed, and a necessary and sufficient condition was given for the direct sum of two -groups to be a -group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable...
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