commutativity degree of zp ≀ zpn

Commutativity degree of $mathbb{Z}_p$≀$mathbb{Z}_{p^n}

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

A Generalization of Commutativity Degree of Finite Groups

on the commutativity degree in finite moufang loops

the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...

Four-manifolds which admit Zp ×Zp actions

We show that the simply-connected four-manifolds which admit locally linear, homologically trivial Zp ×Zp actions are homeomorphic to connected sums of ±CP 2 and S × S (with one exception: pseudofree Z3 × Z3 actions on the Chern manifold), and also establish an equivariant decomposition theorem. This generalizes results from a 1970 paper by Orlik and Raymond about torus actions, and complements...

CONCORDANCE OF Zp × Zp ACTIONS ON S 4

The main result of [7] was that if M is a simply-connected four-manifold admitting an effective, homologically trivial, locally linear action byG = Zp×Zp, where p is prime, then M is equivariantly homeomorphic to a connected sum of standard actions on copies of ±CP 2 and S2 × S2 with a possibly non-standard action on S4. In this note we further examine these non-standard actions on the sphere. ...

AN IMPROVEMENT ON OLSON’S CONSTANT FOR Zp ⊕ Zp

We prove that for a prime number p greater than 6000, the Olson’s constant for the group Zp ⊕ Zp is given by Ol(Zp ⊕ Zp) = p − 1 + Ol(Zp).