### 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 (Electronic) | 9781461464822 |

ISBN (Print) | 9781461464815 |

DOIs | |

State | Published - Jan 1 2013 |

### ASJC Scopus subject areas

- Mathematics(all)

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## 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