Finite groups containing many involutions
Author:
Avinoam Mann
Journal:
Proc. Amer. Math. Soc. 122 (1994), 383385
MSC:
Primary 20D60; Secondary 20C15
MathSciNet review:
1242094
Fulltext PDF Free Access
Abstract 
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Abstract: If the ratio of the number of involutions of a finite group to the group order is bounded below, the group is bounded by abelian by bounded.
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 R. D. Blyth, Rewriting products of group elements. I, J. Algebra 116 (1988), 506521. MR 953167 (90b:20033)
 [BM]
 Y. Berkovich and A. Mann, On sums of degrees of the irreducible characters of a finite group and its subgroups (in preparation).
 [CLMR]
 M. Curzio, P. Longobardi, M. Maj, and D. J. S. Robinson, A permutational property of groups, Arch. Math. 44 (1985), 385389. MR 792360 (86j:20034)
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 I. M. Isaacs, Character theory of finite groups, Academic Press, San Diego, 1976. MR 0460423 (57:417)
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 H. Liebeck and D. MacHale, Groups with automorphisms inverting most elements, Math. Z. 124 (1972), 5163. MR 0291273 (45:367)
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 K. G. Nekrasov and Ya. G. Berkovich, Finite groups with large sums of degrees of irreducible characters, Publ. Math. Debrecen 33 (1986), 333354. (Russian) MR 883763 (88d:20017)
 [P]
 D. Passman, The algebraic structure of group rings, WileyInterscience, New York, 1977. MR 470211 (81d:16001)
 [PMN]
 P. M. Neumann, Two combinatorial problems in group theory, Bull. London Math. Soc. 21 (1989), 456458. MR 1005821 (90f:20036)
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 D. J. Rusin, What is the probability that two elements of a finite group commute, Pacific J. Math. 82 (1979), 237247. MR 549847 (80m:20024)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199412420947
PII:
S 00029939(1994)12420947
Keywords:
Involutions
Article copyright:
© Copyright 1994
American Mathematical Society
