The automorphism group of the power semigroup P(H) of any numerical semigroup H is trivial.
Title resolution pending
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
verdicts
UNVERDICTED 4representative citing papers
Rigidity theorems establish that P(H) ≅ P(K) implies H ≅ K for group H and semigroup K, with the finite-subset version holding only for additive subgroups of the rationals via a diophantine theorem.
The finitary power semigroup of a numerical semigroup S has only the identity automorphism unless S contains all integers from some k onward, in which case its automorphism group is generated by the identity and the involution X maps to max X minus X plus min X.
A survey of the arithmetic properties of power monoids and their role in factorization theory for non-cancellative and non-commutative monoids.
citing papers explorer
-
Power Semigroups and Two Rigidity Theorems for Groups
Rigidity theorems establish that P(H) ≅ P(K) implies H ≅ K for group H and semigroup K, with the finite-subset version holding only for additive subgroups of the rationals via a diophantine theorem.
-
On automorphism groups of power semigroups over numerical semigroups or over numerical monoids
The finitary power semigroup of a numerical semigroup S has only the identity automorphism unless S contains all integers from some k onward, in which case its automorphism group is generated by the identity and the involution X maps to max X minus X plus min X.