Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GASmodule and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P ∗); (3)...

background: cucumber mosaic virus (cmv) from the bromoviridae family, is one of the most widespread plant viruses in the world. objectives: in the present study tomato fields in guilan, isfahan, khorasan razavi, khuzestan and tehran provinces were surveyed to determine the presence of cmv subgroups during 2011-2012. materials and methods: out of 305 symptomatic leaf samples tested by enzyme-lin...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

Background and Aim: There is a gap of information on the effect of time, disinfectant, and storage conditions on the dimensional stability of direct post patterns made of self-cure acrylic resins. This study assessed the effect of Deconex® and wet or dry stor-age conditions on the dimensional stability of post patterns made of Duralay and GC acrylic resins. Materials and Methods: Sixty spe...

Statistical findings on subgroups belong to the most popular and simple forms of knowledge we encounter in all domains of science, business, or even daily life. We are told such messages as: Unemployment rate is overproportionally high for young men with low educational level, young poor women are infected with AIDS at a much higher rate than their male counterparts, lung cancer mortality rate ...

If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...