let $g$ be a group and $x in g$‎. ‎the cyclicizer of $x$ is defined to be the subset $cyc(x)=lbrace y in g mid langle x‎, ‎yrangle ; {rm is ; cyclic} rbrace$‎. ‎$g$ is said to be a tidy group if $cyc(x)$ is a subgroup for all $x in g$‎. ‎we call $g$ to be a c-tidy group if $cyc(x)$ is a cyclic subgroup for all $x in g setminus k(g)$‎, ‎where $k(g)$ is the intersection of all the cyclicizers in ...

a group $g$ is said to be a c-tidy group if for every element $x in g setminus k(g)$‎, ‎the set $cyc(x)=lbrace y in g mid langle x‎, ‎y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $g$‎, ‎where $k(g)=underset{x in g}bigcap cyc(x)$‎. ‎in this short note we determine the structure of finite c-tidy groups‎.

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...

The article introduces cyclic dilation groups and finite affine groups for prime integers, and  as an application of this theory it presents a unified group theoretical approach for the  cyclic wavelet transform (CWT) of prime dimensional periodic signals.

background: there are many concerns regarding the marginal seal of composite restorations, especially when composite restorations are subjected to cyclic loading. the aim of this study was to evaluate the effect of cyclic loading on the microleakage of silorane based composite compared with low shrinkage methacrylate-based composites in class v cavities. materials and methods: in this in vitro ...