The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup

Download or read book The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup written by U. Meierfrankenfeld and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.