arXiv subjects

John Maginnis

Publications and source records attributed to John Maginnis.

6 recordsLinked to original sources

arXiv2011

On the vertices of indecomposable summands of certain Lefschetz modules

We study the reduced Lefschetz module of the complex of p-radical and p-centric subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with central quotient H a finite group of Lie type in characteristic p. A non-projective indecomposable summand of the associated Lefschetz module lies in a non-principal block of G and it is a Green correspondent of an inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this summand is the defect group of the block in which it lies.

math.GR↗

arXiv2008

On fixed point sets and Lefschetz modules for sporadic simple groups

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component of the centralizer. For odd primes, fixed point sets are computed for sporadic groups having an extraspecial Sylow p-subgroup of order p^3, acting on the complex of those p-radical subgroups containing a p-central element in their centers. Vertices for summands of the associated reduced Lefschetz modules are described.

math.GR↗

arXiv2007

On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group McL

We study the homotopy relation between the standard 2-local geometry and the Bouc complex for the sporadic finite simple group McL.

math.GR↗

arXiv2007

New collections of p-subgroups and homology decompositions for classifying spaces of finite groups

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness properties.

math.GR↗

arXiv2007

On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group Co3

We study the homotopy relation between the standard 2-local geometry and the Bouc complex for the sporadic group Co3. We also give a result concerning the relative projectivity of the reduced Lefschetz module associated to the aformentioned 2-local geometry.

math.GR↗

arXiv2007

On fixed point sets of distinguished collections for groups of parabolic characteristic

We determine the nature of the fixed point sets of groups of order p, acting on complexes of distinguished p-subgroups (those p-subgroups containing p-central elements in their centers). The case when G has parabolic characteristic p is analyzed in detail.

math.GR↗