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  • Author or Editor: M. Lawson x
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Abstract  

This paper was inspired by a monograph by Bratteli and Jorgensen, and the work of Kawamura. We introduce two new semigroups: a wide inverse submonoid of the polycyclic inverse monoid, called the gauge inverse monoid, and a Zappa-Szép product of an arbitrary free monoid with the free monoid on one generator. Both these monoids play an important role in studying arbitrary, not necessarily transitive, strong actions of polycyclic inverse monoids. As a special case of such actions, we obtain some new results concerning the strong actions of P 2 on ℤ determined by the choice of one positive odd number. We explain the role played by Lyndon words in characterising these repesentations and show that the structure of the representation can be explained by studying the binary representations of the numbers

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{1} {p},\frac{2} {p}, \ldots \frac{{p - 1}} {p}$$ \end{document}
. We also raise some questions about strong representations of the polycyclic monoids on free abelian groups.

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Abstract

Kanazawa (2007) proposes the ‘evolutionary psychological imagination’ (p.7) as an authoritative framework for understanding complex social and public issues. As a case study of this approach, Kanazawa addresses acts of international terrorism, specifically suicide bombings committed by Muslim men. It is proposed that a comprehensive explanation of such acts can be gained from taking an evolutionary perspective armed with only three points of cultural knowledge: 1. Muslims are exceptionally polygynous, 2. Muslim men believe they will gain reproductive access to 72 virgins if they die as a martyr and 3. Muslim men have limited access to pornography, which might otherwise relieve the tension built up from intra-sexual competition. We agree with Kanazawa that evolutionary models of human behaviour can contribute to our understanding of even the most complex social issues. However, Kanazawa's case study, of what he refers to as ‘World War III’, rests on a flawed theoretical argument, lacks empirical backing, and holds little in the way of explanatory power.

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