On a theorem of Schur.
On almost normal subgroups of supersoluble groups
Un sottogruppo di un gruppo si dice «almost normal» se ha soltanto un numero finito di coniugati in , e ovviamente l'insieme costituito dai sottogruppi almost normal di è un sottoreticolo del reticolo di tutti i sottogruppi di . In questo articolo vengono studiati gli isomorfismi tra reticoli di sottogruppi almost normal, provando in particolare che se è un gruppo supersolubile e è un gruppo FC-risolubile tale che i reticoli e sono isomorfi, allora anche è supersolubile, e...
On an equivalence of fuzzy subgroups. III.
On centralizers of elements of groups acting on trees with inversions.
On certain characterizations of barely transitive groups
On certain closed subgroups of .
On cyclic subgroups of the group .
On D. I. Moldavanskij's question on -separable subgroups of a free group.
On disjoint covering of groups by their cosets
On embedding properties of -groups.
On exact power margin groups
On factor coverings of groups
On finite subgroups of groups of type VF.
On free subgroups of generalized triangle groups.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On genus and embeddings of torsion-free nilpotent groups of class two.
On groups of plolynomial subgroup growth.
On Groups whose Contranormal Subgroups are Normally Complemented
2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.
On groups with many nearly maximal subgroups
A subgroup of a group is nearly maximal if the index is infinite but every subgroup of properly containing has finite index, and the group is called nearly if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly if and only if it is either cyclic or dihedral.