# 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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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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Step 1

Yes, 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)

Step 2

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

Step 3

Again, with the help of group G= (Z2, +) we can construct new group named infinitely generated gro...

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