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The cohomology of finite p-groups plays a crucial role in coclass theory. For instance, the proof of Periodicity I presented in Chapter 7 relies fundamentally on cohomological methods. In this chapter we develop the basic theory of group cohomology from first principles, and build up to the central results required for the applications that follow.

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Cohomology theory and extensions

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  • 发表日期：

    2026年

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  • Heiko Dietrich,
  • Bettina Eick

摘要

The cohomology of finite p-groups plays a crucial role in coclass theory. For instance, the proof of Periodicity I presented in Chapter 7 relies fundamentally on cohomological methods. In this chapter we develop the basic theory of group cohomology from first principles, and build up to the central results required for the applications that follow.