Supersoluble and Related Cofinitary Groups

✍ Scribed by B. A. F. Wehrfritz

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 758 KB
• Volume: 176
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19951760122

✦ Synopsis

Let D be a division ring (possibly commutative) and V an infinite-dimensional left vector space over D. We consider irreducible subgroups G of GL(VJ containing an element whose fixedpoint set in V is non-zero but finite dimensional (over D). We then derive conclusions about cofinitary groups, an element of GL(V) being cofinitary if its fixed-point set is finite dimensional and a subgroup G of GL(V) being cofinitary if all its non-identity elements are confinitary. In particular we show that an irreducible cofinitary subgroup G of G L ( V ) is usually imprimitive if G is supersoluble and is frequently imprimitive if G is hypercyclic. The latter includes the case where G is hypercentral, which apparently is also new.