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COCHAIN SEQUENCES AND THE QUILLEN CATEGORY OF A COCLASS FAMILY

Part of: Representation theory of groups Connections with homological algebra and category theory

Published online by Cambridge University Press:  12 May 2016

BETTINA EICK  and
DAVID J. GREEN
BETTINA EICK
Affiliation:
Institut Computational Mathematics, TU Braunschweig, 38106 Braunschweig, Germany email [email protected]
DAVID J. GREEN*
Affiliation:
Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany email [email protected]
*
✉[email protected]
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Abstract

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We introduce the concept of infinite cochain sequences and initiate a theory of homological algebra for them. We show how these sequences simplify and improve the construction of infinite coclass families (as introduced by Eick and Leedham-Green) and also how they can be applied to prove that almost all groups in such a family have equivalent Quillen categories. We also include some examples of infinite families of $p$-groups from different coclass families that have equivalent Quillen categories.

Keywords

p-groupscoclassQuillen categoryextension class

MSC classification

Primary: 20D15: Nilpotent groups, $p$-groups
Secondary: 20J06: Cohomology of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 2 , April 2017 , pp. 185 - 204
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

Green received travel assistance from DFG grant GR 1585/6-1.

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