Finite groups with prime to the first power

Author:
Zon I Chang

Journal:
Trans. Amer. Math. Soc. **222** (1976), 267-288

MSC:
Primary 20D25

DOI:
https://doi.org/10.1090/S0002-9947-1976-0427464-2

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 3*s*. 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:
https://doi.org/10.1090/S0002-9947-1976-0427464-2

Keywords:
Trivial intersection set,
*p*-blocks of defect 1,
irreducible characters of defect 0

Article copyright:
© Copyright 1976
American Mathematical Society