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Bicyclic Groups

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2127)

Abstract

Bicyclic groups are a natural generalization of metacyclic groups. Here bicyclic means that the group can be written as a product of two cyclic subgroups. In this chapter we classify all saturated fusion systems on bicyclic groups. For odd primes, every bicyclic group is metacyclic and the classification is due to Stancu. In case p = 2 the classification is very delicate. As an application we verify Olsson’s Conjecture for blocks with bicyclic defect groups.

Keywords

  • Maximal Subgroup
  • Irreducible Character
  • Fusion System
  • Commutator Subgroup
  • Defect Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Sambale, B. (2014). Bicyclic Groups. In: Blocks of Finite Groups and Their Invariants. Lecture Notes in Mathematics, vol 2127. Springer, Cham. https://doi.org/10.1007/978-3-319-12006-5_10

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