A parallelogram configuration condition in nets
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .
A precedence theorem for semigroups.
A probabilistic approach to representation formulae for semigroups of operators with rates of convergence.
A Problem in the Theory of Normal Flitting Classes.
A problem of Kollár and Larsen on finite linear groups and crepant resolutions
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...
A Problem of W.A. Manning on Primitive Permutation Groups.
A problem on semigroups satisfying permutation identities.
A projective limit characterization of GIF semigroups with an N-congruence.
-projective resolutions and an Azumaya theorem for a class of mixed abelian groups
A proof of Ph. Hall's theorem on dimension subgroups
A proof of the Montague-Plemmons-Schein Theorem on maximal subgroups of the semigroup of binary relations.
A property equivalent to commutativity for infinite groups
A property equivalent to permutability for groups
A property of -groups
It is shown, under ZFC, that a -group has the interesting property of being -prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on -groups.
A property of Generalized McLain groups
A property of orthodox semigroups.
A property of special representations of Weyl groups.
A property of the Schützenberger product.
A property of the variety of 2-Engel groups
A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent
Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite)...