Isoclinism and stable cohomology of wreath products

Fedor Bogomolov, Christian Böhning

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups (see Theorem 11). Moreover, we show that the stable cohomology of the n-fold wreath product Gn=Z/p…Z/p of cyclic groups Z/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.

Original languageEnglish (US)
Title of host publicationBirational Geometry, Rational Curves, and Arithmetic
PublisherSpringer New York
Pages57-76
Number of pages20
ISBN (Print)9781461464822, 9781461464815
DOIs
StatePublished - Jan 1 2013

Fingerprint

Wreath Product
Cohomology
Finite P-group
Subgroup
Finite Groups of Lie Type
Cyclic group
Fold
Algebra
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bogomolov, F., & Böhning, C. (2013). Isoclinism and stable cohomology of wreath products. In Birational Geometry, Rational Curves, and Arithmetic (pp. 57-76). Springer New York. https://doi.org/10.1007/978-1-4614-6482-2_3

Isoclinism and stable cohomology of wreath products. / Bogomolov, Fedor; Böhning, Christian.

Birational Geometry, Rational Curves, and Arithmetic. Springer New York, 2013. p. 57-76.

Research output: Chapter in Book/Report/Conference proceedingChapter

Bogomolov, F & Böhning, C 2013, Isoclinism and stable cohomology of wreath products. in Birational Geometry, Rational Curves, and Arithmetic. Springer New York, pp. 57-76. https://doi.org/10.1007/978-1-4614-6482-2_3
Bogomolov F, Böhning C. Isoclinism and stable cohomology of wreath products. In Birational Geometry, Rational Curves, and Arithmetic. Springer New York. 2013. p. 57-76 https://doi.org/10.1007/978-1-4614-6482-2_3
Bogomolov, Fedor ; Böhning, Christian. / Isoclinism and stable cohomology of wreath products. Birational Geometry, Rational Curves, and Arithmetic. Springer New York, 2013. pp. 57-76
@inbook{e75c050fa71e4f0999b68aa80f144129,
title = "Isoclinism and stable cohomology of wreath products",
abstract = "Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups (see Theorem 11). Moreover, we show that the stable cohomology of the n-fold wreath product Gn=Z/p…Z/p of cyclic groups Z/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.",
author = "Fedor Bogomolov and Christian B{\"o}hning",
year = "2013",
month = "1",
day = "1",
doi = "10.1007/978-1-4614-6482-2_3",
language = "English (US)",
isbn = "9781461464822",
pages = "57--76",
booktitle = "Birational Geometry, Rational Curves, and Arithmetic",
publisher = "Springer New York",

}

TY - CHAP

T1 - Isoclinism and stable cohomology of wreath products

AU - Bogomolov, Fedor

AU - Böhning, Christian

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups (see Theorem 11). Moreover, we show that the stable cohomology of the n-fold wreath product Gn=Z/p…Z/p of cyclic groups Z/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.

AB - Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups (see Theorem 11). Moreover, we show that the stable cohomology of the n-fold wreath product Gn=Z/p…Z/p of cyclic groups Z/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.

UR - http://www.scopus.com/inward/record.url?scp=84884973704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884973704&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-6482-2_3

DO - 10.1007/978-1-4614-6482-2_3

M3 - Chapter

SN - 9781461464822

SN - 9781461464815

SP - 57

EP - 76

BT - Birational Geometry, Rational Curves, and Arithmetic

PB - Springer New York

ER -