Sylow multiplicities in finite groups
Let $G$ be a finite group and let $mathcal{P}=P_{1},ldots,P_{m}$ be a sequence of Sylow $p_{i}$-subgroups of $G$, where $p_{1},ldots,p_{m}$ are the distinct prime divisors of $leftvert Grightvert $. The Sylow multiplicity of $gin G$ in $mathcal{P}$ is the number of distinct factorizations...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2018-06-01
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| Series: | International Journal of Group Theory |
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| Online Access: | http://ijgt.ui.ac.ir/article_21482_4d16a7d4c6f2488422da19da3ac6bcf6.pdf |
| Summary: | Let $G$ be a finite group and let $mathcal{P}=P_{1},ldots,P_{m}$ be a sequence of Sylow $p_{i}$-subgroups of $G$, where $p_{1},ldots,p_{m}$ are the distinct prime divisors of $leftvert Grightvert $. The Sylow multiplicity of $gin G$ in $mathcal{P}$ is the number of distinct factorizations $g=g_{1}cdots g_{m}$ such that $g_{i}in P_{i}$. We review properties of the solvable radical and the solvable residual of $G$ which are formulated in terms of Sylow multiplicities, and discuss some related open questions. |
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| ISSN: | 2251-7650 2251-7669 |