A subset S of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of S is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, p-groups with large rank relative to the exponent, in...

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study Tits alternative and virtual derived length solvable subgroups $\operatorname{Aut}(X)$.

Classical sieve methods of analytic number theory have recently been adapted to a geometric setting. In the new setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over Z. We will present the method and some of the surprising results that have been proved using it. For instance, the probability that a plane curve ov...

Human serum more strongly depressed the feeding response of Hydra (ball formation) elicited by S-methylglutathione than plasma. On the basis of the effect of several proteins released by platelets, at least five apparent components of the response (R1-R5) were suggested. Each of the platelet proteins examined specifically depressed a subset of these components. Among the platelet proteins exami...

We give a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under taking Brauer construction any subgroup $Q$ of as $k[Q\,C_G(Q)]$-module, where $k$ is field characteristic $2$, and wreathed $2$-subgroup finite group $G$. This generalizes results cases abelian some others. The motivation this paper that indecomposability $p$-permutation bimodule ($p$ prime)...

‎Let $tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$‎. ‎Let $bar{G}=G/H_{G}$ and $bar{H}=H/H_{G}$‎. ‎We say that $H$ is $Phi$-$tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $bar{T}$ of $bar{G}$ and some $tau$-subgroup $bar{S}$ of $bar{G}$ contained in $bar{H}$‎, ‎$bar{H}bar{T}$ is $S$-quasinormal in $bar{G}$ and $bar{H}capbar{T}leq bar{S}Phi(bar{H})$‎. ‎I...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal{h}$-subgroup in‎ ‎$g$ if $n_g(h)cap h^{g}leq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ ‎$mathcal{h}^{ast}$-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal{h}$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎as...

We investigate invariant random subgroups in groups acting on rooted trees. Let $\mathrm{Alt}_f(T)$ be the group of finitary even automorphisms $d$-ary tree $T$. prove that a nontrivial ergodic IRS acts without fixed points boundary $T$ contains level stabilizer, particular it is conjugate finite index subgroup. Applying technique to branch we an regular derived subgroup generalized rigid sta...