Hi everybody! Recently I started reading some articles about the
degree of commutativity of finite groups. I have some questions:

1. In, Subgroup commutativity degrees of finite groups, Tarnauceanu
proposes the following formula for calculating the degree of
commutativity of subgroups of a finite group G:

$$sd(G)= \displaystyle \frac{1}{|\mathscr{L}(G)|^2}\
|\{(H,K)\in\mathscr{L}(G)^2\ |\ HK=KH\}|$$


, he proves in this work  that if


$$G_1, G_2, \ldots , G_n$$  are finite groups of coprime order than

$$ sd(\times_{i=1}^{n}G_{i})=\prod_{i=1}^{n}sd(G_i) $$

My first question is about what  happens if we omit the hypothesis of
$G_i$ have order coprime, that is, exists some  estimative for
$$sd(\times_{i=1}^{n}G_{i})$$
is there any estimate in terms of  $sd(G_i)$

2. In,  Central Extensions and Commutativity Degree, Lescot proposes
the following formula for calculating the degree of commutativity of a
finite group G:

$$d(G)=\frac{1}{|G|^2}|\{(x,y)\in G\times G\;|\;xy=yx\}|.$$

My  second questions is about of order of group $G$, that is,  there
is  any theory for the case that G is infinite? For example if G is a
group equipped with a Haar measure? I found no literature about this
case that G is infinite, there is some technical difficulty in trying
to do something analogous in this case?

Remark: Sorry for the obscurity of my question, the first question is: For $G_1,\ldots,G_n$ arbitrary groups, is there any estimate for the degree of commutativity of subgroups of $G=direct~product~of~the~groups~ G_i$ in terms of the degree of commutativity of the groups $G_i$? My second question was partially answered, a friend showed me the following articles: tmu.ac.ir/salg20/talks/Rezaei.pdf.