# Groups having the same Hall-Senior genus

From Groupprops

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This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.

## Definition

Two groups and are said to have the same **Hall-Senior genus** if there is a lattice isomorphism between their respective lattices of normal subgroups (i.e., a bijection that preserves the containment relationship) such that under this lattice isomorphism, every group is mapped to an isoclinic group.

The term was used in the classification, by Hall and Senior, of the groups of order , and in this context, and are taken to be groups of order for the same .