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GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

  • HOWARD SMITH (a1)
Abstract
Abstract

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a π-group for some finite set π of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

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References
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1.Casolo C., Torsion-free groups in which every subgroup is subnormal, Rend. Circolo Mat. Palermo. L (2001), 321324.
2.Casolo C., On the structure of groups with all subgroups subnormal, J. Group Theory 5 (2002), 293300.
3.Hall P., Some sufficient conditions for a group to be nilpotent, Illinois J. Math. 2 (1958), 787801.
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10.Smith H., Residually nilpotent groups with all subgroups subnormal, J. Algebra. 244 (2001), 845850.
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12.Smith H., Groups that involve finitely many primes and have all subgroups subnormal, J. Algebra. 347 (2011), 133142.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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