2014/09/12 by Alexander Bors, Bors, Alexander
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #05C38 #05C60 #05C76 #05E15 #20D45 #20D60 #37P99 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Gene Regulatory Network Analysis #Group Theory (math.GR) #math.GR #msc:05C38 #msc:05C60 #msc:05C76 #msc:05E15 #msc:20D45 #msc:20D60 #msc:37P99
paper · pdf · doi:10.48550/arxiv.1409.3756
8 pages
openalex publication_date 2014/09/12 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed 1-tree whose cycle is a loop with a disjoint union of cycles, generalizing results of Hernández-Toledo on linear finite dynamical systems, and we fully characterize the possible forms of state spaces of nilpotent endomorphisms via their "ramification behavior". Finally, as an application, we will count the isomorphism types of state spaces of endomorphisms of finite cyclic groups in general, extending results of Hernández-Toledo on primary cyclic groups of odd order.