The structure of irreducible matrix groups with submultiplicative spectrum
Authors:
Marjeta Kramar
Affiliation:
a Faculty of Civil and Geodetic Engineering, Univerity of Ljubljana, 1000 Ljubljana, Sloveniab Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Sloveniac Communicated by R. Guralnick,
Abstract:
We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p2× p2 matrices if p is an odd prime.