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ON GROUPS SATISFYING THE MAXIMAL AND THE MINIMAL CONDITIONS FOR SUBNORMAL SUBGROUPS OF INFINITE ORDER OR INDEX

Alessio Russo
대한수학회 (The Korean Mathematical Society)|2010.07|대한수학회보 (Bulletin of the KMS)|제47권 제4호|pp. 687-691

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키워드

radicalsubnormalmaximal conditionminimal conditionsolublesubsoluble
주제분류수학

초록

In this article we will prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index,respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek in [5].

Abstract

In this article we will prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index,respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek in [5].

참고문헌 (12)

  1. R. Baer, "Polyminimaxgruppen", Math. Ann., 175, pp.1~43 (1968)
  2. F. de Giovanni, "The maximal and minimal conditions for normal subgroups of infinite order or index", Comm. Algebra, 33(1), pp.183~199 (2005)
  3. L. A. Kurdachenko, "Groups that satisfy weak minimality and maximality conditions for normal subgroups", Sibirsk. Mat. Zh., 20(5), pp.1068~1076 (1979)
  4. L. A. Kurdachenko, "Groups satisfying weak minimality and maximality conditions for subnormal subgroups", Mat. Zametki, 29(1), pp.19~30 (1981)
  5. D. H. Paek, "Chain conditions for subnormal subgroups of infinite order or index", Comm. Algebra, 29(7), pp.3069~3081 (2001)
  6. D. H. Paek, "Chain conditions for subgroups of infinite order or index", J. Algebra, 249(2), pp.291~305 (2002)
  7. 박대현, "Locally nilpotent groups with the maximal condition on infinite normal subgroups", 대한수학회보, 41(3), pp.465~472 (2004), 대한수학회
  8. 박대현, "Locally nilpotent groups", 대한수학회보, 41(4), pp.779~783 (2004), 대한수학회
  9. D. J. S. Robinson, "Finiteness Conditions and Generalized Soluble Groups" (1972), Springer-Verlag
  10. D. J. S. Robinson, "On the homology of hypercentral groups", Arch. Math. (Basel), 32(3), pp.223~226 (1979)
  11. D. I. Zaičev, "Groups satisfying a weak minimal condition", Soviet Math. Dokl., 9, pp.194~197 (1968)
  12. D. I. Zaičev, "On groups which satisfy a weak minimal condition", Math. USSR Sb., 7, pp.315~322 (1969)

관련 논문AI추천

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