Abstract group

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The term abstract group is used to refer to a group in the usual sense, with emphasis on the fact that no additional structure beyond the group structure is being referred to.

The term abstract group is typically used in the context of a group with additional structure, such as a topological group, Lie group or algebraic group. For instance, when describing a particular topological group, we may say, as an abstract group, it is defined as ... which means that that sentence only refers to the group structure and not the topology.