From local to global similarity of matrix groups |
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Authors: | Grega Cigler |
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Affiliation: | Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia |
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Abstract: | Let G and H be groups of complex n×n matrices. We say that G is an H-like group if every matrix in G is similar to a matrix from H. For several groups H we consider two questions:- (A)
- Is every H-like group (simultaneously) similar to a subgroup of H?
- (B)
- Is H the only H-like group containing H? Among other results we prove that the symmetric group Sn is the only Sn-like group containing Sn.
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Keywords: | 15A 20B30 |
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