r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

We investigate the automorphisms of some $$\kappa $$ -existentially closed groups. In particular, we prove that Aut(G) is union subgroups level preserving and $$|Aut(G)|=2^{\kappa }$$ whenever inaccessible G unique group cardinality . Indeed, latter result a byproduct an argument showing that, for any uncountable limit regular representation length with countable base, have $$|Aut(G)|=\beth _{\...

In this paper we study the distribution of eigenvalues of regular graphs , regular hypergraphs , and biregular bipartite graphs of given girth by considering the polynomials orthogonal with respect to the measures attached to the spectra of such graphs and to the continuous spectra of their ‘universal covers’ . Our estimates are tight for Biggs graphs and generalized polygons . We also give an ...

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

In this paper we study intrinsic regular submanifolds of \(\mathbf{H}^n\) low codimension in relation with the regularity their parametrization. We extend some results proved for \(\mathbf{H}\)-regular surfaces 1 to \(k\), \(1 \leq k n\). characterize uniformly differentiable functions, \(\phi\), acting between two complementary subgroups Heisenberg group \(\mathbf{H}^n\), target space horizont...

in this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. we study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

Let G=Cpn be a finite cyclic p-group, and let Hol(G) denote its holomorph. In this work, we find characterize the regular subgroups of that mutually normalize each other in symmetric group Sym(G). We represent as vertices graph, connect pair them by an edge when they other. The approach to construct local normalizing graph relies on theory gamma functions, final result will contain all informat...

The interplay between set-theoretic solutions of the Yang--Baxter equation Mathematical Physics, skew braces, regular subgroups, and Hopf--Galois structures has spawned a considerable body literature in recent years. In paper, Alan Koch generalised construction Lindsay N.~Childs, showing how one can obtain bi-skew braces $(G, \cdot, \circ)$ from an endomorphism group \cdot)$ whose image is abel...