Let KG be the group algebra of a group G over a field K of positive characteristic p, and let D((n)) (G) and D([n]) (G) denote the n-th upper Lie dimension subgroup and the n-th lower one, respectively. In [1] and [12], the equality D((n)) (G) = D([n]) (G) is verified when p >= 5. Motivated by [16, Problem 55], in the present paper we establish it for particular classes of groups when p <= 3. Finally, we introduce and study a new central series of G linked with the Lie nilpotency class of KG.
Lie Dimension Subgroups and Central Series Related to Group Algebras / Spinelli, Ernesto. - In: ALGEBRA COLLOQUIUM. - ISSN 1005-3867. - STAMPA. - 16:3(2009), pp. 427-436.
Lie Dimension Subgroups and Central Series Related to Group Algebras
SPINELLI, ERNESTO
2009
Abstract
Let KG be the group algebra of a group G over a field K of positive characteristic p, and let D((n)) (G) and D([n]) (G) denote the n-th upper Lie dimension subgroup and the n-th lower one, respectively. In [1] and [12], the equality D((n)) (G) = D([n]) (G) is verified when p >= 5. Motivated by [16, Problem 55], in the present paper we establish it for particular classes of groups when p <= 3. Finally, we introduce and study a new central series of G linked with the Lie nilpotency class of KG.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
