A combinatorial problem in infinite groups.
A computer algebra solution to a problem in finite groups.
We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
A condition on a certain variety of groups
A non-commutative free algebra of rank 0
A property of the variety of 2-Engel groups
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A Specialization Theorem for Certain Weyl Group Representations and an Application to the Green Polynomials of Unitary Groups.
Algebraic sets and coordinate groups for a free nilpotent group of nilpotency class 2.
All subvarieties of have finite bases of identities.
An elementary proof that finite groups are projectively torsion-free
Automorphismes et deformations des varietes de Borel
Calculation of Baer-invariant of Certain Groups.
Centraliser dimension and universal classes of groups.
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
-тождества и -многообразия
-тождества нильпотентных групп. I
-тождества нильпотентных групп. II
Groups in which certain equations have many solutions
Gruppi con identità semigruppali: su una congettura di M. V. Sapir
M. V. Sapir ha formulato la seguente congettura: non esiste un semigruppo infinito, finitamente generabile, soddisfacente l'identità e immagine omomorfa di un sottosemigruppo di un gruppo nilpotente. Se ciò vale, ogni gruppo risolubile con una base finita per le sue identità semigruppali è abeliano o di esponente finito. In questo lavoro si prova la congettura di Sapir quando l'interderivato è periodico o se è -generato e è periodico.
Gruppi minimali non in