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Minimal rank of abelian group matrices. (English) Zbl 0960.15003

The minimal rank of abelian group matrices with positive integral entries is determined. The corresponding problem for circulant matrices has been investigated by A. W. Ingeleton [J. London Math. Soc. 31, 445-460 (1956; Zbl 0072.00802)] and more recently by W. C. Shiu, S. L. Ma and K. T. Fang [Linear Multilinear Algebra 40, No. 2, 183-188 (1995; Zbl 0857.05015)]. The paper can be viewed as a generalization of their results, since a group matrix becomes circulant when the group is cyclic.

MSC:

15A03 Vector spaces, linear dependence, rank, lineability
15B36 Matrices of integers
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
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