Finite groups with prime to the first power
Author:
Zon I Chang
Journal:
Trans. Amer. Math. Soc. 222 (1976), 267288
MSC:
Primary 20D25
MathSciNet review:
0427464
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Abstract: Earlier D. G. Higman classified the finite groups of order n, such that n is divisible by 3 to the first power, with the assumption that the centralizer of X, where X is a subgroup of order 3, is a cyclic trivial intersection set of even order 3s. In this paper the theorem is generalized to include all prime numbers greater than 3. With an additional assumption: , we have proved that one of the following holds for these groups, hereafter designated as G: (A) G is isomorphic to , where ; (B) there exists a normal subgroup of odd index in G, and a normal subgroup N of of index 2 such that where .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197604274642
PII:
S 00029947(1976)04274642
Keywords:
Trivial intersection set,
pblocks of defect 1,
irreducible characters of defect 0
Article copyright:
© Copyright 1976
American Mathematical Society
