ON GROUPS WHOSE PROPER SUBGROUPS ARE CHERNIKOV-BY-BAER OR (PERIODIC DIVISIBLE ABELIAN)-BY-BAER

ARIKAN A., Trabelsi N.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.12, sa.6, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 6
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1142/s0219498813500151
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Chernikov, divisible, nilpotent, Baer
  • Gazi Üniversitesi Adresli: Evet

Özet

If X is a class of groups, then a group G is called a minimal non-X-group if it is not an X-group but all of its proper subgroups belong to X. In this paper we prove that locally graded minimal non-(Chernikov-by-nilpotent)-groups are precisely minimal non-nilpotent-groups without maximal subgroups and that locally graded minimal non-(Chernikov-by-Baer)-groups are locally finite and coincide with the normal closure of an element. We also prove that an infinite locally graded minimal non-((periodic divisible abelian)-by-Baer)-group G is an imperfect locally nilpotent p-group, for some prime p, and there is an element a in G such that G = < a >(G).