A combinatorial problem in infinite groups.
A remark on growth relation.
Abelian Extensions of Arbitrary Fields.
Alcune proprietà gruppali invarianti per semi-isomorfismi
An application of Ramsey's theory to partition in groups. - II
Bicartesian Squares of Nilpotent Groups.
Circles in (B, N)-Groups.
Complete metacyclic groups
Computing Adams operations on the Burnside ring of a finite group.
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Corrigendum to: "Aspherical four-manifolds and the centres of two-knot groups".
Die maximale lokale Erklärung einer gesättigten Formation
Endliche minkowskische Ebenen von Charakteristik ... 2.
Extensions of Certain Homomorphisms of Subsemi-groups to Homomorphisms of Groups
Extensions of homomorphisms of subsemigroups of a group.
Groups whose proper subgroups are locally finite-by-nilpotent
If is a class of groups, then a group is said to be minimal non -group if all its proper subgroups are in the class , but itself is not an -group. The main result of this note is that if is an integer and if is a minimal non (respectively, )-group, then is a finitely generated perfect group which has no non-trivial finite factor and such that is an infinite simple group; where (respectively, , ) denotes the class of nilpotent (respectively, nilpotent of class at most , locally...
Homology theory in the alternative set theory I. Algebraic preliminaries
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris
The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.
Hyper–(Abelian–by–finite) groups with many subgroups of finite depth
The main result of this note is that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent if and only if every infinite subset contains two distinct elements , such that
Inert actions on periodic points.