Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc97718/eng.pdf Дата изменения: Mon Oct 1 23:27:54 2012 Дата индексирования: Mon Oct 1 23:27:54 2012 Кодировка:

A CONDITION SUFFICIENT FOR NILPOTENCY IN GROUPS Andreev K.K. Moscow State Institute for Electronics and Mathematics, Russia, 109028, Moscow, B. Tryohsvyatitel'skiy pereulok, 3/12, telephone: (499) 246-28-51, E-mail: kirill.andreyev@yandex.ru In my old paper [1] two theorems were proved. Theorem 1. Let G be a tortion-free group, in which every three elements generate a nilpotent subgroup of a bounded class. Then the group G is locally nilpotent. Theorem 2. Let G be a group possessing non-trivial elements of finite order. If every three elements in G generate a nilpotent subgroup of a small class (i. e. less than the order of every non-trivial periodic element of the group), then the group G is locally nilpotent. In the present work I strengthen the theorem 1. Theorem 3. Let G be a tortion-free group, in which every three elements generate a nilpotent subgroup of a bounded class. Then the group G is nilpotent. Reference. 1. Andreev K.K. Some sufficient conditions for local nilpotence in groups. //TrudyMIEM. Mathematical Analysis and Its Applications, issue 30. Moscow, MIEM, 1974. Pp. 19-43. (In Russian.)