The object of this note is to give a very short proof of the following theorem of Ivanov and Schupp. Let H be a finitely generated subgroup of a free group F and the index [F : H ] infinite. Then there exists a nontrivial normal subgroup N of F such that N ∩ H = {1}. As noted in the abstract above the object of this note is to give a new proof of the following theorem of S.V.Ivanov and P.E.Schu...

‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...

in this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. after obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. the number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. by exploiting the order, we label the s...

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

Three building complexes in Kuala Lumpur were surveyed for the presence of legionellae in cooling towers. The organisms were grown from 12 out of 46 samples of water collected from 30 towers. L. pneumophila serogroups 1 and 7 were the commonest serogroups isolated. None belonged to the Pontiac subgroup of L. pneumophila serogroup 1.

Listeria monocytogenes lineage III strains belonging to subgroups IIIA (n = 8), IIIB (n = 5), and IIIC (n = 6) were examined along with other known serotype strains (n = 11) by PCR and Southern hybridization using several recently described species-, virulence-, and serotype-specific primers and probes. The virulence of seven representative lineage III strains was then evaluated in mice via the...

We prove that any Hecke eigenclass in the mod p cohomology of a congruence subgroup of GL(1,Z) or GL(2,Z) has attached to it a mod p Galois representation such that the characteristic polynomial of a Frobenius element at a prime l equals the Hecke polynomial at l.

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...