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Adjoint groups of finite rings

Version 1.6.6

25 February 2023

Olexandr Konovalov
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Panagiotis Soules
Department of Mathematics
National and Capodistrian University of Athens
Panepistimioupolis, GR-15784, Athens, Greece


The GAP4 package Circle extends the GAP functionality for computations in adjoint groups of associative rings. It provides functionality to construct circle objects that will respect the circle multiplication \( r \cdot s = r + s + rs \), and to compute adjoint semigroups and adjoint groups of finite rings. Also it may serve as an example of extending the GAP system with new multiplicative objects.


© 2006-2023 by Olexandr Konovalov and Panagiotis Soules

Circle is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF's own site

If you obtained Circle, we would be grateful for a short notification sent to one of the authors.

If you publish a result which was partially obtained with the usage of Circle, please cite it in the following form:

O. Konovalov, P. Soules. Circle --- Adjoint groups of finite rings, Version 1.6.6; 2023 (


We acknowledge very much Alexander Hulpke and James Mitchell for their helpful comments and advices, and the referee for testing the package and useful suggestions.


1 Introduction
2 Implementing circle objects
3 Circle functions
4 A sample computation with Circle

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