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On the dynamics of endomorphisms of finite groups

Content Provider	Springer Nature Link
Author	Bors, Alexander
Copyright Year	2016
Abstract	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.
Ending Page	214
Page Count	10
Starting Page	205
File Format	PDF
ISSN	09381279
e-ISSN	14320622
Journal	Applicable Algebra in Engineering, Communication and Computing
Issue Number	3
Volume Number	28
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-09-17
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) Group endomorphisms Graph operations (line graphs, products, etc.) State space Theory of Computation Automorphisms Finite group Computer Hardware Combinatorial aspects of groups and algebras Artificial Intelligence (incl. Robotics) Finite dynamical system Symbolic and Algebraic Manipulation Paths and cycles Arithmetic and combinatorial problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory

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