the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

t he purpose of this study was to examine farm operations cooperation groups in central agricultural zone of delta state, nigeria. all the members of the six  selected groups were used for the study. the data which were collected with the use of questionnaire and interview schedule were analyzed with the use of frequency counts, percentages and tobit regression model. most of the members were ...

for any group g, let c(g) denote the set of centralizers of g.we say that a group g has n centralizers (g is a cn-group) if |c(g)| = n.in this note, we prove that every finite cn-group with n ≤ 21 is soluble andthis estimate is sharp. moreover, we prove that every finite cn-group with|g| < 30n+1519 is non-nilpotent soluble. this result gives a partial answer to aconjecture raised by a. ashrafi in ...

a positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free burnside groups of sufficiently large odd periods $n>10^{10}$ obtained previously by s. v. ivanov and r. mikhailov extended to all odd periods $ngeq 665$‎.

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

let $cr_{n}(f)$ denote the algebra of $n times n$ circulant matrices over the field $f$. in this paper, we study the unit group of $cr_{n}(f_{p^m})$, where $f_{p^m}$ denotes the galois field of order $p^{m}$, $p$ prime.