On the structure of lower bounded HNN extensions

This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semi groups, as introduced by Jajcayov & aacute;. We show that if S-* = [S; U-1, U-2; f] 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-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 R-classes, residual finiteness, being E-unitary, and 0 -E-unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.