Additivity of the algebraic entropy for locally finite groups with\n permutable finite subgroups

2020/01/08 by Anna Giordano Bruno, Flavio Salizzoni, Bruno, Anna Giordano +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Protein Tyrosine Phosphatases #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2001.02419

openalex publication_date 2020/01/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The additivity with respect to exact sequences is notoriously a fundamental\nproperty of the algebraic entropy of group endomorphisms. It was proved for\nabelian groups by deeply exploiting their structure. On the other hand, a\nsolvable counterexample was recently found, showing that it does not hold in\ngeneral. Nevertheless, we give a rather short proof of the additivity of the\nalgebraic entropy for locally finite groups that are either quasihamiltonian or\nFC-groups.\n

Related

• Entropy on abelian groups
• Algebraic entropy on topologically quasihamiltonian groups
• The Addition theorem for two-step nilpotent torsion groups
• Limit free computation of entropy
• Topological Entropy and Algebraic Entropy for group endomorphisms