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Centers of Sylow subgroups and automorphisms
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-09-23 , DOI: 10.1007/s11856-020-2064-2
George Glauberman , Robert Guralnick , Justin Lynd , Gabriel Navarro

Suppose that p is an odd prime and G is a finite group having no normal non-trivial p'-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner. This answers a conjecture of Gross.

中文翻译:

Sylow 子群和自同构的中心

假设 p 是一个奇素数,G 是一个有限群,没有正规的非平凡 p'-子群。我们证明如果 a 是集中 G 的 Sylow p 群的 p 幂阶 G 的自同构,则 a 是内在的。这回答了格罗斯的猜想。
更新日期:2020-09-23
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