A fast isomorphism test for groups whose Lie algebra has genus 2

A Lie Algebra for Frölicher Groups

Frölicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C∞(M, G) or Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Frölicher groups. One can define tangent spaces...

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups

Sperm DNA damage assessment: a test whose time has come.

Multiple techniques have been developed to measure the amount of sperm DNA damage in an effort to identify more objective parameters for evaluation of infertile men. We now have evidence to support that integrity of sperm DNA influences a couple's fertility and helps predict the chances of pregnancy and its successful outcome. The available tests of sperm DNA damage require additional large-sca...