We describe the subgroups of the group Zm × Zn × Zr and derive a simple formula for the total number s(m,n, r) of the subgroups, where m,n, r are arbitrary positive integers. An asymptotic formula for the function n 7→ s(n, n, n) is also deduced.

BACKGROUNDS Segmental and circumferential pulmonary vein isolations (SPVI and CPVI) have been demonstrated to be effective therapies for paroxysmal atrial fibrillation (PAF). PVI is well established as the endpoint of different ablation techniques, whereas it may not completely account for the long-term success. METHODS 181 drug-refractory symptomatic PAF patients were referred for segmental ...

In this paper, we introduce the notion of (i-v) fuzzy (weakly) completely regular subsemigroup of a semigroup S and study their different properties. We show that every (i-v) fuzzy completely regular subsemigroup of a semigroup S is a union of (i-v) fuzzy subgroups of S. We also characterize (i-v) fuzzy completely regular subsemigroup by (i-v) fuzzy semilattice of (i-v) fuzzy subgroups. 2010 AM...

In this note we give examples of a ring that has no maximal ideals. Recall that, by a Zorn’s lemma argument, a ring with identity has a maximal ideal. Therefore, we need to produce examples of rings without identity. To help motivate our examples, let S be a ring without identity. We may embed S in a ring R with identity so that S is an ideal of R. Notably, set R = Z⊕S, as groups, and where mul...

In this paper, we prove the p-nilpotency of a finite group with assumption that some subgroups of Sylow subgroup are weakly s-semipermutable subgroups in the normalizer of Sylow subgroups. Our results unify and generalize some earlier results. Mathematics Subject Classification: 20D10, 20D15

In the theory of one-relator groups, Magnus subgroups, which are free subgroups obtained by omitting a generator that occurs in the given relator, play an essential structural role. In a previous article, the author proved that if two distinct Magnus subgroups M and N of a one-relator group, with free bases S and T are given, then the intersection of M and N is either the free subgroup P genera...

Silvestri, L. G. (Università Statale, Milan, Italy), and L. R. Hill. Agreement between deoxyribonucleic acid base composition and taxometric classification of gram-positive cocci. J. Bacteriol. 90:136-140. 1965.-It had been previously proposed, from taxometric analyses, that gram-positive, catalase-positive cocci be divided into two subgroups. Thirteen strains, representative of both subgroups,...