Catene pronormali nei gruppi finiti supersolubili
Characters and systems of subgroups.
Classification of finite groups satisfying a minimal condition.
Classification of finite groups with many minimal subgroups and with the number of conjugacy classes of G/S(G) equal to 8.
In this paper we classify all the finite groups satisfying r(G/S(G))=8 and ß(G)=r(G) - a(G) - 1, where r(G) is the number of conjugacy classes of G, ß(G) is the number of minimal normal subgroups of G, S(G) the socle of G and a(G) the number of conjugacy classes of G out of S(G). These results are a contribution to the general problem of the classification of the finite groups according to the number of conjugacy classes.
Counting with groups and rings.
Die Untergruppenstruktur der Gruppen mit quadratfreier Ordnung.
Die Untergruppenverbände von Gruppen, deren Ordnungen höchstens drei Primfaktoren enthalten.
Dual-Standard subgroups of finite and locally finite groups.
Endliche Gruppen mit vielen Untergruppen.
Erratum to: “Solitary quotients of finite groups”
In this short note a correct proof of Theorem 3.3 from [Tărnăuceanu M., Solitary quotients of finite groups, Cent. Eur. J. Math., 2012, 10(2), 740–747] is given.
Exact covering systems for groups
Finite Groups as the Union of Proper Subgroups
2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum...
Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index.
Finite groups whose poset of conjugacy classes of subgroups is isomorphic to the one of an abelian group
Si determinano i gruppi finiti il cui insieme parzialmente ordinato delle classi di coniugio dei sottogruppi è isomorfo a quello di un gruppo abeliano.
Finite groups with few conjugacy classes of subgroups
Finite groups with globally permutable lattice of subgroups
The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they have a description...
Finite groups with modular chains
In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.
Fonction de Möbius d'un groupe fini et anneau de Burnside.
Formations generated by a group of socle length 2.
Generic Fixed Point Free Action of Arbitrary Finite Groups.