Left residual operator for composition
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Suppose are two subgroup properties. The left residual of by is the unique subgroup property such that:
Here, denotes the composition operator.
Statement with symbols
Suppose are two subgroup properties. The left residual of by is defined as the subgroup property as follows:
has property in if whenever is embedded as a subgroup with property in a group , has property in .
Relation with left transiter
Further information: Left transiter
The left transiter of a subgroup property is defined as the left residual of by itself.