• Corpus ID: 237372485

Hierarchical Complexity of Finite Groups

  title={Hierarchical Complexity of Finite Groups},
  author={Chrystopher L. Nehaniv},
What are simplest ways to construct a finite group from its atomic constituents? To understand part-whole relations between finite simple groups (“atoms”) and the global structure of finite groups, we axiomatize complexity measures on finite groups. From the Jordan-Hölder theorem and Frobenius-Lagrange embedding in an iterated wreath product, any finite group G can be constructed from a unique collection of simple groups, its Jordan-Hölder factors, each with well-defined multiplicities through… 



The q-theory of Finite Semigroups

Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other

Cascade Product of Permutation Groups

We define the cascade product of permutation groups as an external product, an explicit construction of substructures of the iterated wreath product that are much smaller than the full wreath

Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Biology

This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century and sets the stage for the application of algebraic automata theory to areas outside mathematics.

A Course in the Theory of Groups

This is a detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the

SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of


  • K. KrohnJ. Rhodes
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1965
The purpose of this short note is to announce the major results of papersl1 2 which will be published elsewhere. All undefined notation of this note can be found in reference 3. 1. Prime

The Evolution and Understanding of Hierarchical Complexity in Biology from an Algebraic Perspective

It is proved that in a smooth sequence of t inclusion steps, complexity may grow at most from N to .N C 1/t C N, a linear function of number of generations t, while for sequences of mapping steps it increases by at most t.

Permutation groups