Residually finite group
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In mathematics, in the realm of group theory, a group is said to be residually finite or finitely approximable if for each nonidentity element in the group, there is a normal subgroup of finite index not containing that element. Equivalently, a group is residually finite if and only if it can be embedded inside the direct product of a set of finite groups.
One question is: what are the properties of a variety all of whose groups are finitely approximable? Two results about these are:
- Any variety comprising only residually finite groups is generated by an A group.
- For any variety comprising only residually finite groups, it contains a finite group such that all members are embedded in a direct product of that finite group.
