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The converse of Glauberman's ZJ-theorem
Prof. Jianbei An(安建碚)(University of Auckland, New Zealand)
2018-01-01 12:13  华东师范大学

曹锡华数学论坛

题目:The converse of Glauberman's ZJ-theorem
时间:2011年12月19日(星期一)下午3:00
地点:数学楼报告厅(102)
报告人:Prof. Jianbei An (University of Auckland, New Zealand)

摘要:
Let $G$ be finite group, $p$ an odd prime factor of the order $|G|$ of $G$ and $S$ a Sylow $p$-subgroup of $G$. Glauberman's ZJ-theorem states that if $G$ has no subquotient isomorphic to a quodratic group, then $N(Z(J(S)))$ controls $p$-fusion of $G$, where the quodratic group is the semidirect product $p^2{:}SL_2(p)$ of elementary abelian group $p*2$ and the special linear group $SL_2(p)$ (with natural action of $SL_2(p)$ on $p^2$), and $Z(J(S))$ is the center of the Thompson subgroup $J(S)$ of $S$.

Glauberman's ZJ-theorem is one of the very important theorems in the finite group theory.

In this talk I'll discuss the converse of Glauberman's theorem. The talk is based on my two research papers.