In group theory (abstract algebra), is there a special name given either to the group, or the elements themselves, if x^2=e for all x?

In group theory (abstract algebra), is there a special name given either to the group, or the elements themselves, if ${x}^{2}=e$ for all x?
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Aubree Mcintyre

There is a special name given either to the group, or the elements themselves, if ${x}^{2}=e$ for all x. In group theory, there are certain group which named as finitely or infinitely generated group. Here, some few examples: Boolean group (which all elements has self-inverse)
Let $G=\left({Z}_{2},+\right)$ be group whose all elements has order one or two. Then with the help of group G we can construct the new group named finitely generated group G’ has elements whose order is either one or two such that
${G}^{\prime }={\mathbb{Z}}_{2}×{\mathbb{Z}}_{2}×{\mathbb{Z}}_{2}×\dots ×{\mathbb{Z}}_{2}$
$←$ n-times $\to$
Again, with the help of group $G=\left({Z}_{2},+\right)$ we can construct new group named infinitely generated group named S’ has elements whose order is either one or two such that
$S={\mathbb{Z}}_{2}×{\mathbb{Z}}_{2}×{\mathbb{Z}}_{2}×\dots ×{\mathbb{Z}}_{2}$
$←$ infinite-times $\to$
There are some group named as Klein’s group which is finitely generated group.
$K=\left\{e,a,b,ab\right\}$