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.

On the basis of an initial interest in symmetric cryptography, present work we study a chain subgroups. Starting from Sylow $2$-subgroup AGL(2,n), each term is defined as normalizer previous one group on $2^n$ letters. Partial results and computational experiments lead us to conjecture that, for large values $n$, index consecutive does not depend $n$. Indeed, there strong evidence that sequence...

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...

A group G is (finitely) co-Hopfian if it does not contain any proper (finite-index) subgroups isomorphic to itself. We study finitely generated groups that admit a descending chain of normal finite-index subgroups, each which G. prove up finite index, these are always obtained by pulling back from free abelian quotient. give two applications: First, we show characteristic subgroup arises the ab...

a normal subgroup $n$ of a group $g$ is said to be an‎ ‎$emph{omissible}$ subgroup of $g$ if it has the following property‎: ‎whenever $xleq g$ is such that $g=xn$‎, ‎then $g=x$‎. ‎in this note we construct various groups $g$‎, ‎each of which has an omissible subgroup $nneq 1$ such that $g/ncong sl_2(k)$ where $k$ is a field of positive characteristic‎.