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===Fixed-point operator=== A group is a fixed-point under the FC-center operator if and only ... ...

===The fixed-point operator=== The fixed-point operator is a map from the collection of quotient ... ...

true with respect to the composition operator. That is, p is t.i. if e ... with respect to the composition operator arises as follows. Consider ... ...

===Fixed-point operator=== A group equals its Wielandt subgroup if and only if every subnormal subgroup of the group is normal, or equivalently ... ...

===The fixed-point operator=== The fixed-point operator is a map from the collection of subgroup ... ...

An example of a subgroup property modifier is the subordination operator ... property. We are also interested in the fixed-point space: the collection ... ...

The extensibility operator is a map from the function property space ... The extensibility operator E is a map from the function property space ... ...

The left transiter is an operator from the subgroup property space ... where * denotes the composition operator on subgroup properties. ... ...

The subordination operator is a map from the subgroup property space ... The subordination operator on a property p gives the following property: ... ...

The intermediately operator is a map from the subgroup property space ... The intermediately operator is idempotent, in the sense that applying ... ...

of something || the normal closure operator is idempotent, so its image ... the whole group under the normal closure operator is the set of contranormal ... ...

===Fixed-point operator=== A group is its own Fitting subgroup if and only if it is a Fitting group. For finite groups, this is equivalent to ... ...

===Fixed-point operator=== A group equals its own centralizer of commutator subgroup if and only if it is nilpotent of class two. ==Subgroup-defining ... ...

Applying the upward closure operator twice is the same as applying it once. In other words, the properties that are fixed under the upward closure ... ...

master theorem for the composition operator on subgroup properties. ... Together, (3) and (4) tell us that the left transiter operator is ... ...

The in-normalizer operator is a map from the subgroup property space ... Important instances of application of the in-normalizer operator: ... ...

The locally operator is a map from the group property space to itself ... The locally operator is a map from the group property space to itself ... ...

===Fixed-point operator=== A group equals its own Frattini subgroup if and only if it has no maximal subgroups. For instance, the group of rational ... ...

condition if and only if it is a fixed-point of the idempotent subgroup ... condition if and only if it is a fixed-point of the idempotent subgroup ... ...

==Description== ===Setup=== Let G be a group with an encoding C. That is, C associates to each element of G a string over a fixed (say, binary ... ...