### 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 G_{n}=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 language | English (US) |
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Title of host publication | Birational Geometry, Rational Curves, and Arithmetic |

Publisher | Springer New York |

Pages | 57-76 |

Number of pages | 20 |

ISBN (Print) | 9781461464822, 9781461464815 |

DOIs | |

State | Published - Jan 1 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Birational Geometry, Rational Curves, and Arithmetic.*Springer New York, pp. 57-76. https://doi.org/10.1007/978-1-4614-6482-2_3

}

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 -