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2 results

  • ON THE NUMBER OF PRIME ORDER SUBGROUPS OF FINITE GROUPS

  • Part of
  • TIMOTHY C. BURNESS, STUART D. SCOTT
  • Journal:
    Journal of the Australian Mathematical Society / Volume 87 / Issue 3 / December 2009
    Published online by Cambridge University Press:
    15 December 2009, pp. 329-357
    Print publication:
    December 2009
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  • Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G)≥∣G∣/2−1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order.

  • ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS

  • Erhard Aichinger
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001
    Published online by Cambridge University Press:
    20 January 2009, pp. 379-388
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  • Let $N$ be a zero-symmetric near-ring with identity, and let $\sGa$ be a faithful tame $N$-group. We characterize those ideals of $\sGa$ that are the range of some idempotent element of $N$. Using these idempotents, we show that the polynomials on the direct product of the finite $\sOm$-groups $V_1,V_2,\dots,V_n$ can be studied componentwise if and only if $\prod_{i=1}^nV_i$ has no skew congruences.

    AMS 2000 Mathematics subject classification: Primary 16Y30. Secondary 08A40