Length Functions and HNN Groups
Faisal H. Nesayef *
Department of Mathematics, Faculty of Science, University of Kirkuk, Kirkuk, Iraq.
*Author to whom correspondence should be addressed.
Abstract
The concept of length functions on groups is first introduced by Lyndon. This is used to give direct proofs of many other results in combinatorial group theory. Two important sets called M and N satisfying some certain axioms of length functions are considered. Finally investigations of the nature and the structures of the sets M and N in relation to the elements of HNN group were carried out.
Keywords: Archimedean elements, associated subgroups, conjugate elements, Coset representative, H. N. N extension, isomorphism, length functions, normal form, reduced word.