Weights for $π$-partial characters of $π$-separable groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866907876681842688 |
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| author | Chang, Xuewu Jin, Ping |
| author_facet | Chang, Xuewu Jin, Ping |
| contents | The aim of this paper is to confirm an inequality predicted by Isaacs and Navarro in 1995, which asserts that for any $π'$-subgroup $Q$ of a $π$-separable group $G$, the number of $π'$-weights of $G$ with $Q$ as the first component always exceeds that of irreducible $π$-partial characters of $G$ with $Q$ as their vertex. We also give some sufficient condition to guarantee that these two numbers are equal, and thereby strengthen their main theorem on the $π$-version of the Alperin weight conjecture. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_14125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weights for $π$-partial characters of $π$-separable groups Chang, Xuewu Jin, Ping Group Theory Representation Theory 20C15, 20C20 The aim of this paper is to confirm an inequality predicted by Isaacs and Navarro in 1995, which asserts that for any $π'$-subgroup $Q$ of a $π$-separable group $G$, the number of $π'$-weights of $G$ with $Q$ as the first component always exceeds that of irreducible $π$-partial characters of $G$ with $Q$ as their vertex. We also give some sufficient condition to guarantee that these two numbers are equal, and thereby strengthen their main theorem on the $π$-version of the Alperin weight conjecture. |
| title | Weights for $π$-partial characters of $π$-separable groups |
| topic | Group Theory Representation Theory 20C15, 20C20 |
| url | https://arxiv.org/abs/2404.14125 |