We show some results on the probability that a randomly picked pair (H, K) of subgroups of a
finite group G satisfies [H, K]= 1. This notion of probability is related with the subgroup S …

The present paper is a note on the relative tensor degree of finite groups. This notion
generalizes the tensor degree, introduced recently in literature, and allows us to adapt the …

Using the notion of complete nonabelian exterior square Ĝ∧ G of a pro-p-group G (p
prime), we develop the theory of the exterior degree ̂d (G) in the infinite case, focusing on …

The commutativity degree of finite groups is computed by finding the number of conjugacy
classes of G. Also, finding the centralizers of a finite group can be applied to obtain the …

In 2009 M. Tarnauceanu introduced the concept of subgroup commutativity degree of a finite
group G. This concept is arising interest in several areas of group theory in the last years. In …

The commutativity degree, defined as the probability that two randomly selected elements of
a group commute, plays a very important role in determining the abelianness of a group. In …

‎ Let $ G $ be a finite group and $ d_2 (G) $ denotes the probability‎‎ that $[x, y, y]= 1$ for
randomly chosen elements $ x, y $ of $ G $‎.‎ We‎‎ will obtain lower and upper bounds for …

We correlate the notion of 𝑛-isoclinism of finite groups, introduced by JC Bioch in 1976, with
the relative 𝑛-th nilpotency degree, recently studied in literature. We characterize also all the …

Given a finite group 𝐺, we introduce the permutability degree of 𝐺, as pd (G)= 1| G|| 𝓛 (G)|∑
X∈ 𝓛 (G)| PG (X)|, where 𝓛 (𝐺) is the subgroup lattice of 𝐺 and 𝑃𝐺 (𝑋) the permutizer of the …

On the commutativity degree of metacyclic groups of 5-power order using conjugation action
Page 1 Zamri et al. / Malaysian Journal of Fundamental and Applied Sciences Vol. 13, No. 4 …