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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
View other such properties
Suppose are groups. We say that is subset-conjugacy-determined in , or that fusion of subsets of in is contained in , if whenever and is such that , there exists such that for all .
If is subset-conjugacy-determined in itself relative to , we say that is a subset-conjugacy-closed subgroup.
Relation with other properties
- Conjugacy-determined subgroup
- Normal subset-conjugacy-determined subgroup
- Weak normal subset-conjugacy-determined subgroup
Related subgroup properties
- Subset-conjugacy-closed subgroup: A subgroup that is subset-conjugacy-determined in itself relative to the whole group.
- SCDIN-subgroup: A subgroup that is subset-conjugacy-determined in its normalizer, relative to the whole group.