A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.

Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.

  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 we...

for any given finite abelian group‎, ‎we give factorizations of the group determinant in the group algebra of any subgroups‎. ‎the factorizations is an extension of dedekind's theorem‎. ‎the extension leads to a generalization of dedekind's theorem‎.

let l = u3(9) be the simple projective unitary group in dimension 3 over a eld with 92 elements. in this article, we classify groups with the same order and degree pattern as an almost simple group related to l. since aut(l) = z4 hence almost simple groups related to l are l, l : 2 or l : 4. in fact, we prove that l, l : 2 and l : 4 are od-characterizable.

a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is ‎cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq‎ ‎z(g)$‎. ‎in this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{cac}$-$p$-groups‎.

‎the purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the fischer matrices and the ordinary‎ ‎character table of the split extension $overline{g}=‎ ‎3^{7}{:}sp(6,2)$ by means of clifford-fischer theory‎. ‎we firstly‎‎determine the conjugacy classes of $overline{g}$ using the coset‎ ‎analysis method‎. ‎the determination of the inertia factor groups of‎ ‎...

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let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

in this paper we give some general results on the non-splitextension group $overline{g}_{n} = 2^{2n}{^{cdot}}sp(2n,2), ngeq2.$ we then focus on the group $overline{g}_{4} =2^{8}{^{cdot}}sp(8,2).$ we construct $overline{g}_{4}$ as apermutation group acting on 512 points. the conjugacy classes aredetermined using the coset analysis technique. then we determine theinertia factor groups and fischer...