<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Delgado, Manuel</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Solvable monoids with commuting idempotents</style></title><secondary-title><style face="normal" font="default" size="100%">Int. J. Algebra Comput.</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Maltsev products</style></keyword><keyword><style  face="normal" font="default" size="100%">pseudo-varieties of aperiodic semigroups}</style></keyword><keyword><style  face="normal" font="default" size="100%">pseudo-varieties of groups</style></keyword><keyword><style  face="normal" font="default" size="100%">solvable finite semigroups</style></keyword><keyword><style  face="normal" font="default" size="100%">solvable groups</style></keyword><keyword><style  face="normal" font="default" size="100%">{Abelian kernels</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">547-570</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The notion of the Abelian kernel of a finite monoid is a generalization of that of the derived subgroup of a finite group. A monoid $M$ is then called solvable if its chain of Abelian kernels terminates with the submonoid of $M$ generated by its idempotents. The main result of this paper is that the finite idempotent commuting monoids bearing this property are precisely those whose subgroups are solvable. In particular any finite aperiodic monoid is Abelian-solvable in this sense. A generalization of the main result of this paper has been published [in Int. J. Algebra Comput. 14, No. 5-6, 655-665 (2004; Zbl 1081.20067)] by the authors and ıt S. Margolis and ıt B. Steinberg.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
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