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Simple groups of order $ 2\sp{a}3\sp{b}5\sp{c}7\sp{d}p$


Author: Leo J. Alex
Journal: Trans. Amer. Math. Soc. 173 (1972), 389-399
MSC: Primary 20D05
DOI: https://doi.org/10.1090/S0002-9947-1972-0318291-1
MathSciNet review: 0318291
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Abstract: Let $ {\operatorname{PSL}}(n,q)$ denote the projective special linear group of degree $ n$ over $ {\text{GF}}(q)$, the field with $ q$ elements. The following theorem is proved. Theorem. Let $ G$ be a simple group of order $ {2^a}{3^b}{5^c}{7^d}p,a > 0,p$ an odd prime. If the index of a Sylow $ p$-subgroup of $ G$ in its normalizer is two, then $ G$ is isomorphic to one of the groups, $ {\operatorname{PSL}}(2,5),{\operatorname{PSL}}(2,7),{\operatorname{PSL}}(2,9),... ...\operatorname{PSL}}(2,25),{\operatorname{PSL}}(2,27),{\operatorname{PSL}}(2,81)$, and $ {\operatorname{PSL}}(3,4)$.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0318291-1
Keywords: Finite simple group classification, class algebra coefficient, characters of finite groups, principal $ p$-block
Article copyright: © Copyright 1972 American Mathematical Society

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