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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 727–734 (Mi mz7793)  

Infinite groups satisfying the normalizer condition for nonprimary subgroups

K. Sh. Kemkhadze

Mathematics Institute, Academy of Sciences of the Ukrainian SSR

Abstract: In this paper we study infinite groups satisfying the normalizer condition for nonprimary subgroups. We show, in particular, that a nonprimary periodic group satisfying this condition is locally finite if the intersection of all its nonprimary subgroups is finite. We establish the local nilpotency of a nonperiodic group satisfying the normalizer condition for nonprimary subgroups. This implies the theorem of S. N. Chernikov which states that a nonperiodic group in which each infinite proper subgroup is different from its normalizer satisfies the normalizer condition.

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English version:
Mathematical Notes, 1976, 19:5, 434–437

Bibliographic databases:

UDC: 519.4
Received: 17.07.1975

Citation: K. Sh. Kemkhadze, “Infinite groups satisfying the normalizer condition for nonprimary subgroups”, Mat. Zametki, 19:5 (1976), 727–734; Math. Notes, 19:5 (1976), 434–437

Citation in format AMSBIB
\Bibitem{Kem76}
\by K.~Sh.~Kemkhadze
\paper Infinite groups satisfying the normalizer condition for nonprimary subgroups
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 727--734
\mathnet{http://mi.mathnet.ru/mz7793}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=422426}
\zmath{https://zbmath.org/?q=an:0356.20032}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 434--437
\crossref{https://doi.org/10.1007/BF01142566}


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