The method of constructing the generalized dihedral group as a semidirect product an abelian and Z2 integers modulo 2 is extended to case gyrogroups. This leads study new class gyrogroups, which includes groups special case. In this article, we show that any dihedralizable gyrogroup can be enlarged dihedralized gyrogroup. Then, establish algebraic properties gyrogroups well combinatorial their ...

In this paper we consider the conformal group of the unit sphere S, the proper Lorentz group Spin(1, n), for the study of spherical continuous wavelet transforms. The parameter space is determined by the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We study two families of sections that give rise to anisotropic conformal dilation operators for the unit sphere...

In this paper, we have studied the properties of associated gyrogroup °G a given group G nilpotency class 3. We proved that if 3 does not divide order G, then ni...

In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, give a gyrogroup version factor group lemma and show that some certain gyrogroups are Hamiltonian.

A space X is submaximal if any dense subset of open. In this paper, we prove that every topological gyrogroup non-measurable cardinality strongly ?-discrete. Moreover, hereditarily paracompact.

in this paper we characterize the radical of an arbitrary‎ ‎submodule $n$ of a finitely generated free module $f$ over a‎ ‎commutatitve ring $r$ with identity‎. ‎also we study submodules of‎ ‎$f$ which satisfy the radical formula‎. ‎finally we derive‎ ‎necessary and sufficient conditions for $r$ to be a‎ ‎pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $rbigopl...