in this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{a}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{a}(t)) dt +mathbf{c}$. we also observe that the effective force $mathbf{f}_e$ on that particle due to pseudo-force $mathbf{a}(t)$, is given by $ mathbf{f}_e= mathbf{f} mat...

In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.

In this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{A}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{A}(t)) dt +mathbf{c}$. We also observe that the effective force $mathbf{F}_e$ on that particle due to pseudo-force $mathbf{A}(t)$, is given by $ mathbf{F}_e= mathbf{F} mat...

In this paper, we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two.

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...

This article explores possibilities of partitioning the vertex set of a given simple loop-free Sperner hypergraph into a union of transversals. Studies are done on the possible number of transversals in such partitions, followed by forming a hypergraph (on the vertex set of the given hypergraph) that consists of transversals for hyperedges. AMS Subject Classification: 05C65

A latin square of order n is an n×n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries containing no pair of entries that share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutuall...

We completely describe the structure of the connected components of transversals to a collection of n line segments in R. We show that n > 3 arbitrary line segments in R admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.

We completely describe the structure of the connected components of transversals to a collection of n arbitrary line segments in R. We show that n 3 line segments in R admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.