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- W2950988081 abstract "Let $G$ be a finite group and $G_p$ be a Sylow $p$-subgroup of $G$ for a prime $p$ in $pi(G)$, the set of all prime divisors of the order of $G$. The automiser $A_p(G)$ is defined to be the group $N_G(G_p)/G_pC_G(G_p)$. We define the Sylow graph $Gamma_A(G)$ of the group $G$, with set of vertices $pi(G)$, as follows: Two vertices $p,qinpi(G)$ form an edge of $Gamma_A(G)$ if either $qinpi(A_p(G))$ or $pin pi(A_q(G))$. The following result is obtained: Theorem: Let $G$ be a finite almost simple group. Then the graph $Gamma_A(G)$ is connected and has diameter at most 5. We also show how this result can be applied to derive information on the structure of a group from the normalizers of its Sylow subgroups." @default.
- W2950988081 created "2019-06-27" @default.
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- W2950988081 date "2009-12-15" @default.
- W2950988081 modified "2023-09-27" @default.
- W2950988081 title "On the Sylow graph of a group and Sylow normalizers" @default.
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