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 Mat. Zametki: Year: Volume: Issue: Page: Find

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

Infinite groups satisfying the normalizer condition for nonprimary subgroups

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

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}