This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.
Being isologic can roughly be thought as being congruent modulo , i.e., the difference between the groups lives in . In this sense, it behaves like congruence mod n.
- Any group in is isologic to the trivial group.
- Isologism with respect to variety is isologism with respect to any bigger variety
- Isologic groups with respect to fixed nilpotency class lower than theirs have equal nilpotency class
|Variety||Corresponding notion of isologic groups|
|variety containing only the trivial subgroup||isomorphic groups (this is the finest possible notion of isologism)|
|variety of abelian groups||isoclinic groups|
|variety of nilpotent groups of class at most||fixed-class isologic groups|
|variety of all groups||any two groups are isologic with this relation (this is the coarsest possible notion of isologism)|