A. Caranti

GRADED LIE ALGEBRAS OF MAXIMAL CLASS

We study graded Lie algebras of maximal class over a field

Quotients of maximal class of thin Lie algebras. The odd characteristic case

\mathbf {F}

Some thin Lie algebras related to Albert-Frank algebras and algebras of maximal class

of positive characteristic

Loop algebras of Zassenhaus algebras in characteristic three

p

Graded Lie algebras of maximal class. V

. A. Shalev has constructed infinitely many pairwise non-isomorphic insoluble algebras of this kind, thus showing that these algebras are more complicated than might be suggested by considering only associated Lie algebras of p-groups of maximal class. Here we construct

Analyticity and Growth of Pro-p-Groups

| \mathbf {F}|^{\aleph _{0}}

Presenting the Graded Lie Algebra Associated to the Nottingham Group

pairwise non-isomorphic such algebras, and

METABELIAN THIN p-GROUPS

\max \{| \mathbf {F}|, \aleph _{0} \}

Thin Groups of Prime-Power Order and Thin Lie Algebras: An Addendum

soluble ones. Both numbers are shown to be best possible. We also exhibit classes of examples with a non-periodic structure. As in the case of groups, two-step centralizers play an important role

The modular group algebras of

Among thin graded Lie algebras, which are particular instances of Lie algebras of finite width, there are many interesting objects, such as the graded Lie algebra associated to the Nottingham group. Among the factors of a thin algebra with respect to the terms of the lower central series, there is a greatest factor which is of maximal class. In thin Lie algebras associated to groups, this factor is metabelian. In this paper we show that the same holds in general, provided the characteristic of the underlying field is odd. In another paper by the second author it is shown that this is not the case for characteristic two.