In this paper we present a comprehensive survey and developments of existing literature of
non-associative rings and enumerate some of their various applications in different …

The isomorphism problem for finite groups of order n (GpI) has long been known to be
solvable in n^\logn+O(1) time, but only recently were polynomial-time algorithms designed …

We consider the structure of groups and algebras that can be represented as
automorphisms, respectively derivations, of bilinear maps. Representations of that sort arise …

Filters were introduced by JB Wilson in 2013 to generalize work of Lazard with associated
graded Lie rings. It holds promise in improving isomorphism tests, but the formulas …

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients
in a field $ K $, whose determinant describes a smooth cubic in the projective plane. To …

Like the lower central series of a nilpotent group, filters generalize the connection between
nilpotent groups and graded Lie rings. However, unlike the case with the lower central …

Let p be an odd prime and let G be a non-abelian finite p-group of exponent p2 with three
distinct characteristic subgroups, namely 1, Gp and G. The quotient group G/Gp gives rise to …

In studying nilpotent groups, the lower central series and other variations can be used to
construct an associated ℤ+-graded Lie ring, which is a powerful method to inspect a group …

We generalize the common notion of descending and ascending central series. The
descending approach determines a naturally graded Lie ring and the ascending version …

Like the lower central series of a nilpotent group, filters generalize the connection between
nilpotent groups and graded Lie rings. However, unlike the case with the lower central …