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Abstract An LR-structure on a Lie algebra 𝔤 is a bilinear product on 𝔤, satisfying certain commutativity relations, and which is compatible with the Lie product. LR-structures arise in the study of simply transitive affine actions on Lie groups. In particular one is interested in the...
Abstract Let 𝔉 denote the class of finite groups, and let 𝔓 denote the subclass consisting of groups of prime-power order. We study group actions on topological spaces in which all stabilizers lie either in 𝔓 or in 𝔉. We compare the classifying spaces for actions with stabilizers in...
Abstract We prove that a residually nilpotent group with all subgroups subnormal is hypercentral and we bound the hypercentral length of a hypercentral group with all subgroups subnormal.
Abstract Let G be an exceptional algebraic group, X a maximal rank reductive subgroup and P a parabolic subgroup. This paper classifies when X \ G / P is finite. Finiteness is proven using a reduction to finite groups and character theory. Infiniteness is proven using a dimension criterion that...
Abstract Let S be a finite simple group, and the class of poly- S groups, that is, finite groups with all composition factors isomorphic to S . A pro- S group is defined to be an inverse limit of poly- S groups. If S = C p , the finite cyclic group of order p , we get the familiar pro- p groups....
Abstract If * : G → G is an involution on the finite group G , then * extends to an involution on the integral group ring ℤ( G ). In this paper, we consider whether bicyclic units u ∈ ℤ( G ) exist with the property that the group 〈 u, u *〉 generated by u and u * is free on the two...
Abstract We prove that the universal covering of an alternating group Alt( n ) which is Hurwitz is still Hurwitz, with 31 exceptions, 30 of which are detectable by the genus formula.
Abstract This paper is concerned with the ( p 1 , p 2 , p 3 )-generation of finite groups of Lie type, where we say that a group is ( p 1 , p 2 , p 3 )-generated if it is generated by two elements of orders p 1 , p 2 having product of order p 3 . Given a triple ( p 1 , p 2 , p 3 ) of primes, we...
Abstract We show that, given a saturated fusion system, it is, under certain conditions, possible to identify SL 2 ( q ) acting on a natural module inside the normalizer of an essential subgroup. In particular, this is the case if the fusion system is non-constrained and has only one conjugacy...
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