Character degrees of normally monomial ๐-groups of maximal class
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Dongfang Yang
Abstract
A finite group ๐บ is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of ๐บ. In this paper, we study the largest irreducible character degree and the maximal abelian normal subgroup of normally monomial ๐-groups of maximal class in terms of ๐. In particular, we determine all possible irreducible character degree sets of normally monomial 5-groups of maximal class.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971391
Award Identifier / Grant number: 12071376
Funding statement: This research is supported by the National Natural Science Foundation of China (No. 11971391, 12071376). The first author is supported by the Chinese Scholarship Council.
Acknowledgements
The authors would like to thank the referee for her or his valuable suggestions and useful comments on this paper. They also thank Professor Silvio Dolfi for many useful conversations on this topic. The first author is supported by the China Scholarship Council (CSC), whose support is very much appreciated.
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Communicated by: Bettina Eick
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Articles in the same Issue
- Frontmatter
- Curvature distribution and hyperbolicity
- On Whiteheadโs cut vertex lemma
- Abelian splittings and JSJ-decompositions of finitely presented BestvinaโBrady groups
- On endomorphisms of the direct product of two free groups
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The
- A note on torsion length and torsion subgroups
- On the separability of subgroups of nilpotent groups by root classes of groups
- The Addition Theorem for two-step nilpotent torsion groups
- A bound for the orders of centralizers of irreducible subgroups of algebraic groups
- The average character degree of finite groups and Gluckโs conjecture
- Character degrees of normally monomial ๐-groups of maximal class
- Finite groups with an affine map of large order
- Classification of non-solvable groups whose power graph is a cograph
