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One of the most important problems in group theory is proving that a given group is not simple, or even more ambitiously, showing that the group is solvable. The elementary considerations described in Chapter I, §8 and the subsequent exercises are not widely applicable. However, there are two powerful techniques available: In this chapter, we consider the method of monomial representations and transfer. An approach using character theory is discussed in Chapter V and Volume 2.

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Transfer and p-nilpotent groups

  • 章节

  • 发表日期：

    2025年

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  • Bertram Huppert

摘要

One of the most important problems in group theory is proving that a given group is not simple, or even more ambitiously, showing that the group is solvable. The elementary considerations described in Chapter I, §8 and the subsequent exercises are not widely applicable. However, there are two powerful techniques available: In this chapter, we consider the method of monomial representations and transfer. An approach using character theory is discussed in Chapter V and Volume 2.