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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 51 NO.3 / (1999))
Nilpotency of Some Lie Algebras Associated with $p$-Groups
Pavel Shumyatsky,
Pages. 658-672
Abstract Let $L=L_0+L_1$ be a $mathbb Z_2$-graded Lie algebra over a commutative ring with unity in which 2 is invertible. Suppose that $L_0$ is abelian and $L$ is generated by finitely many homogeneous elements $a_1,...,a_k$ such that every
commutator in $a_1,...,a_k$ is ad-nilpotent. We prove that $L$ is nilpotent.
This implies that any periodic residually finite 2'-group $G$ admitting an
involutory automorphism $phi$ with $C_G(phi)$ abelian is locally finite.
Contents 0. Introduction
1. Existence of a nilpotent ideal
2. A sufficient condition for $[L,L]$ to be nilpotent
3. Existence of commuting ideals
4. Main theorem
5. On residually finite groups
Key words
Mathmatical Subject Classification 17B70, 20F50