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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On roots and subsemigroups of nilpotent groups


Author: Joseph E. Kuczkowski
Journal: Proc. Amer. Math. Soc. 28 (1971), 50-52
MSC: Primary 20.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0274585-4
MathSciNet review: 0274585
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Abstract: ${E_\omega },{U_\omega }$ and ${D_\omega }$ semigroups are defined by extrapolating the definitions of their group counterparts; and a class $n$ semigroup is defined to be a subsemigroup of a class $n$ group. The purpose of this paper is to show that a class $n{E_\omega }$ semigroup generates an ${E_\omega }$ group and that a class $n$ semigroup is ${U_\omega }$ if and only if it generates a ${U_\omega }$ group.


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Keywords: <!– MATH ${E_\omega }$ –> <IMG WIDTH="32" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img5.gif" ALT="${E_\omega }$"> semigroup, <!– MATH ${U_\omega }$ –> <IMG WIDTH="31" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="${U_\omega }$"> semigroup, <!– MATH ${D_\omega }$ –> <IMG WIDTH="34" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="${D_\omega }$"> semigroup, <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="$\omega$">-free group, <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\omega$">-subgroup
Article copyright: © Copyright 1971 American Mathematical Society