On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

Groups with Decomposable Set of Quasinormal Subgroups

A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.

Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.

Rough Maximal Oscillatory Singular Integral Operators

2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

Variational Principles for Monotone and Maximal Bifunctions

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

Sequences of Maximal Degree Vertices in Graphs

2000 Mathematics Subject Classification: 05C35.

Kneser and Hereditarily Kneser Subgroups of a Profinite Group

2000 Mathematics Subject Classification: 20E18, 12G05, 12F10, 12F99.

Minimal Subspaces with Maximal Dimensioanal Diameters

Владимир Тодоров - Нека X е компактно метрично пространство с dim X = n. Тогава за n − 1 - мерния диаметър dn−1(X) на X е изпълнено неравенството dn−1(X) > 0, докато dn(X) = 0 (да отбележим, че това е една от характеристиките на размерността на Лебег). От тук се получава, че X съдържа минимално по включване затворено подмножество Y , за което dn−1(Y ) = dn−1(X). Известен резултат е, че от това следва, че Y е Канторово Многообразие. В тази бележка доказваме, че всяко такова (минимално) подпространство Y е даже континуум V^n. Получени са също така някои следствия.