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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Finite groups with prime $p$ to the first power
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by Zon I Chang PDF
Trans. Amer. Math. Soc. 222 (1976), 267-288 Request permission

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 ${C_G}(X)$ 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: $|{N_G}(X):{C_G}(X)| = 2$, we have proved that one of the following holds for these groups, hereafter designated as G: (A) G is isomorphic to ${L_2}(q)$, where $q = 2ps \pm 1$; (B) there exists a normal subgroup ${G_0}$ of odd index in G, and a normal subgroup N of ${G_0}$ of index 2 such that $G = N\langle \sigma \rangle$ where ${C_G}(X) = X \times \langle \sigma \rangle$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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