Lie-Nilpotency Indices of Group Algebras

Lie Properties of the Group Algebra and the Nilpotency Class of the Group of Units

“…s Im , which immediately implies A ( A. 1 Now consider the effect of the automorphism ␣ in case m s m . 2 We conclude that after performing the automorphism ␣ with m s m…”

“…1 i w x By Birkhoff's result 2 any automorphism of P can be effected by a Ž finite succession of the automorphisms fixing each of the basis elements . but one…”

Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

“…Now, we prove that p ≤ 3. Indeed, supposing that p ≥ 5 and G is not cyclic, we can apply [1] and (c) of Lemma 1…”

“…. , x n ∈ R. By induction, we define the n-th upper Lie power R (n) of R as the associative ideal generated by all the Lie commutators [x, y], where R (1) = R and x ∈ R (n−1) , y ∈ R. The algebra R is called Lie nilpotent (respectively, upper Lie nilpotent) if there exists m such that R [m] = 0 (R (m) = 0). The minimal integers m, n such that R [m] = 0 and R (n) = 0 are called the Lie nilpotency index and the upper Lie nilpotency index of R and they are denoted by t L (R) and t L (R), respectively.…”

On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group

“…It was proved in [8] that, for arbitrary group algebras over the field of characteristic p > 3, the nilpotency indices are equal. The same is also true in the case under consideration.…”