For a finite group $G$ and $U: = U(\mathbb{Z}G)$, the of units integral ring $G$, we study implications structure on abelianization $U/U'$ $U$. We pose questions connections between exponent $G/G'$ as well ranks torsion-free parts $Z(U)$, center $U$, $U/U'$. show that originating from known generic constructions in $\mathbb{Z}G$ are well-behaved under projection $U$ to our have positive answer ...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

background and objective: tubal sterilization is the most popular method of permanent female contraception, yet there is considerable debate concerning the influence of this procedure on the women’s health and menstrual pattern.   methods: we randomized 1358 women to one of the five methods of tubal sterilization; unipolar electrocauterization, bipolar electrocauterization, minilaparatomy, pome...

In the mol-ecule of the title compound, C(17)H(15)N(5)O(3)S, the planar central heterocylic ring system is oriented at dihedral angles of 5.32 (4) and 9.41 (4)°, respectively with respect to trimethoxy-phenyl and pyridine rings. Intra-molecular C-H⋯N, C-H⋯O and C-H⋯S hydrogen bonds result in the formation of a nearly planar six-membered ring, which is oriented at a dihedral angle of 3.07 (5)° w...