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OverviewLet p be a prime. In this paper we investigate finite K{2,p}-groups G which have a subgroup H ? G such that K ? H = NG(K) ? Aut(K) for K a simple group of Lie type in characteristic p, and |G : H| is coprime to p. If G is of local characteristic p, then G is called almost of Lie type in characteristic p. Here G is of local characteristic p means that for all nontrivial p-subgroups P of G, and Q the largest normal p-subgroup in NG(P) we have the containment CG(Q) ? Q. We determine details of the structure of groups which are almost of Lie type in characteristic p. In particular, in the case that the rank of K is at least 3 we prove that G = H. If H has rank 2 and K is not PSL3(p) we determine all the examples where G = H. We further investigate the situation above in which G is of parabolic characteristic p. This is a weaker assumption than local characteristic p. In this case, especially when p ? {2, 3}, many more examples appear. In the appendices we compile a catalogue of results about the simple groups with proofs. These results may be of independent interest. Full Product DetailsAuthor: Chris Parker , Gerald Pientka , Andreas Seidel , Gernot StrothPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: Volume: 292 Number: 1452 Weight: 0.272kg ISBN: 9781470467296ISBN 10: 1470467291 Pages: 182 Publication Date: 29 February 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationChris Parker, University of Birmingham, United Kingdom. Gerald Pientka, Halle, Germany. Andreas Seidel, Magdeburg, Germany. Gernot Stroth, Universitat Halle-Wittenberg, Germany. Tab Content 6Author Website:Countries AvailableAll regions |