Fetching the paper…

Reading the bibliography…

2013

Cascade Product of Permutation Groups

Egri-Nagy, Attila, Nehaniv, Chrystopher L.

Original
PDF
Post on X

Understand

Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension.

It is the most general hierarchical product that uses arbitrary total functions to combine a linearly ordered set of permutation groups.
Algebraically speaking, cascade products are explicitly constructed substructures of the iterated wreath product.
We show how direct, semidirect and wreath products can be described as cascade products and we also discuss examples of composite groups that can only be constructed exactly as generic extensions by cascade products.

Cascade Product of Permutation Groups · Around

Built on

Practical Decomposition of Automata
Akihiro Nozaki · 1978
Earlier work this paper cites.
Generalized wreath products of permutation groups
R. A. Bailey, Cheryl E. Praeger, C. A. Rowley, and T. P. Speed · 1983
Earlier work this paper cites.
Cascade Decomposition of Arbitrary Semigroups
Chrystopher L. Nehaniv · 1995
Earlier work this paper cites.
Permutation Groups
John D. Dixon and Brian Mortimer · 1996
Earlier work this paper cites.

Similar

Permutation Groups
Peter J. Cameron · 1999
Cited alongside, same era.
Handbook of Algebra
Laurent Bartholdi, Rostislav I. Grigorchuk, and Zoran Šunić · 2003
Cited alongside, same era.
Algebraic Theory of Finite Automata Networks: An Introduction
Pál Dömösi and Chrystopher L. Nehaniv · 2005
Cited alongside, same era.
Self-Similar Groups
Volodymyr Nekrashevych · 2005
Cited alongside, same era.

Then

The q-theory of Finite Semigroups
John Rhodes and Benjamin Steinberg · 2008
Later among the works it cites.
SgpDec – software package for Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups, Version 0.9.3
Attila Egri-Nagy, Chrystopher L. Nehaniv, and James D. Mitchell · 2021
Closest in time.
GAP – Groups, Algorithms, and Programming, Version 4.11.1
The GAP Group · 2021
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…