To-day we should say that they had dealt with isomorphic groups.
A group may be represented as isomorphic with itself by transforming all its operations by any one of them.
isomorphic i·so·mor·phic (ī'sə-môr'fĭk)
Having a similar structure or appearance but being of different ancestry.
Related by an isomorphism.
Two mathematical objects are isomorphic if they have the same structure, i.e. if there is an isomorphism between them. For every component of one there is a corresponding component of the other.