On the structure of lower bounded HNN extensions
Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 697-715
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This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if $S^* = [ S;\; U_1,U_2;\; \phi ]$ is a lower bounded HNN extension then the maximal subgroups of $S^*$ may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the $\mathcal{D}$-classes of $S$, $U_1$ and $U_2$. We then obtain a number of results concerning when inverse semigroup properties are preserved under the HNN extension construction. The properties considered are completely semisimpleness, having finite $\mathcal{R}$-classes, residual finiteness, being $E$-unitary, and $0$-$E$-unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.
Mots-clés :
inverse semigroups, HNN extensions, Schutzenberger automata, completely semisimple, maximal subgroups
Bennett, Paul; Jajcayová, Tatiana B. On the structure of lower bounded HNN extensions. Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 697-715. doi: 10.1017/S001708952300023X
@article{10_1017_S001708952300023X,
author = {Bennett, Paul and Jajcayov\'a, Tatiana B.},
title = {On the structure of lower bounded {HNN} extensions},
journal = {Glasgow mathematical journal},
pages = {697--715},
year = {2023},
volume = {65},
number = {3},
doi = {10.1017/S001708952300023X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708952300023X/}
}
TY - JOUR AU - Bennett, Paul AU - Jajcayová, Tatiana B. TI - On the structure of lower bounded HNN extensions JO - Glasgow mathematical journal PY - 2023 SP - 697 EP - 715 VL - 65 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S001708952300023X/ DO - 10.1017/S001708952300023X ID - 10_1017_S001708952300023X ER -
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