@article {
author = {Levy, Dan},
title = {Sylow multiplicities in finite groups},
journal = {International Journal of Group Theory},
volume = {7},
number = {2},
pages = {1-8},
year = {2018},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2017.21482},
abstract = {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 $\left\vert G\right\vert $. The Sylow multiplicity of $g\in G$ 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.},
keywords = {Sylow sequences,Sylow multiplicities,Solvable radical,Solvable residual},
url = {https://ijgt.ui.ac.ir/article_21482.html},
eprint = {https://ijgt.ui.ac.ir/article_21482_4d16a7d4c6f2488422da19da3ac6bcf6.pdf}
}