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?

arenceabigns 2021-01-19 Answered
In group theory (abstract algebra), is there a special name given either to the group, or the elements themselves, if x2=e for all x?
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Aubree Mcintyre
Answered 2021-01-20 Author has 73 answers

There is a special name given either to the group, or the elements themselves, if x2=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=(Z2,+) 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=Z2×Z2×Z2××Z2
n-times
Again, with the help of group G=(Z2,+) we can construct new group named infinitely generated group named S’ has elements whose order is either one or two such that
S=Z2×Z2×Z2××Z2
infinite-times
There are some group named as Klein’s group which is finitely generated group.
K={e,a,b,ab}

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