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On direct sums of ( 1 ) -groups

Claudia Metelli — 1993

Commentationes Mathematicae Universitatis Carolinae

A necessary and sufficient condition is given for the direct sum of two ( 1 ) -groups to be (quasi-isomorphic to) a ( 1 ) -group. A ( 1 ) -group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.

A transvection decomposition in GL(n,2)

Clorinda De VivoClaudia Metelli — 2002

Colloquium Mathematicae

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 direct sums of B ( 1 ) -groups – II

Clorinda De VivoClaudia Metelli — 2006

Commentationes Mathematicae Universitatis Carolinae

B ( 1 ) -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 B ( 1 ) -groups was discussed, and a necessary and sufficient condition was given for the direct sum of two B ( 1 ) -groups to be a B ( 1 ) -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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