Finite groups with a proper -generated core

Author:
Michael Aschbacher

Journal:
Trans. Amer. Math. Soc. **197** (1974), 87-112

MSC:
Primary 20D05

DOI:
https://doi.org/10.1090/S0002-9947-1974-0364427-8

MathSciNet review:
0364427

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Abstract: H. Bender's classification of finite groups with a strongly embedded subgroup is an important tool in the study of finite simple groups. This paper proves two theorems which classify finite groups containing subgroups with similar but somewhat weaker embedding properties. The first theorem, classifying the groups of the title, is useful in connection with signalizer functor theory. The second theorem classifies a certain subclass of the class of finite groups possessing a permutation representation in which some involution fixes a unique point.

**[1]**J. Alperin, R. Brauer and D. Gorenstein,*Finite groups of*2-*rank*2 (to appear). MR**0284499 (44:1724)****[2]**H. Bender,*Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festlässt*, J. Algebra**17**(1971), 527-554. MR**44**#5370. MR**0288172 (44:5370)****[3]**D. Gorenstein and K. Harada,*On finite groups with Sylow*2-*subgroups of type*, n = 8, 9, 10, 11, Math. Z.**117**(1970), 207-238. MR**0276348 (43:2095)****[4]**-,*Finite simple groups of low*2-*rank and the families*,*q odd*, Bull. Amer. Math. Soc.**77**(1971), 829-862. MR**46**#5427. MR**0306301 (46:5427)****[5]**-,*Finite groups whose Sylow*2-*subgroups are the direct product of two dihedral groups*, Ann. of Math.**95**(1972), 1-54. MR**0313384 (47:1939)****[6]**-,*Finite groups of sectional*2-*rank at most four*(to appear).**[7]**D. Gorenstein and J. H. Walter,*Centralizers of involutions in balanced groups*, J. Algebra**20**(1972), 284-319. MR**45**#2008. MR**0292927 (45:2008)****[8]**E. Shult,*On the fusion of an involution in its centralizer*(to appear).**[9]**J. G. Thompson,*Fixed points of p-groups acting on p-groups*, Math. Z.**86**(1964), 12-13. MR**29**#5911. MR**0168653 (29:5911)****[10]**J. H. Walter,*The characterization of finite groups with abelian Sylow*2-*subgroups*, Ann. of Math. (2)**89**(1969), 405-514. MR**40**#2749. MR**0249504 (40:2749)****[11]**M. Suzuki,*Applications of group characters*, Proc. Sympos. Pure Math., vol. 6, Amer. Math. Soc., Providence, R. I., 1962, pp. 101-105. MR**24**#A3196. MR**0133362 (24:A3196)**

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0364427-8

Article copyright:
© Copyright 1974
American Mathematical Society