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Some classes of groups with the weak minimality and maximality conditions for normal subgroups

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Abstract

This paper deals with groups satisfying the weak minimality (maximality) condition for normal subgroups and having an ascending series of normal subgroups whose factors are finite or Abelian of finite rank. It is proved that if G is such a group, then it contains a periodic hypercentral normal subgroup H satisfying the Min-G condition such that G/H is minimax and almost solvable.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1050–1056, August, 1990.

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Kurdachenko, L.A. Some classes of groups with the weak minimality and maximality conditions for normal subgroups. Ukr Math J 42, 936–942 (1990). https://doi.org/10.1007/BF01099224

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Keywords

  • Normal Subgroup
  • Maximality Condition
  • Finite Rank
  • Weak Minimality