Monoids on groups with BN-pairs (Q1824704)

Three axioms connecting the idempotent structure of monoids with their group of units G are given. A monoid satisfying these axioms is called a monoid on G. The aim of the paper is to determine all types of maps \(\lambda\) connecting the idempotent structure of monoids on G with G. Main attention is paid to regular monoids on G whose constructions are specified in more detail. A classification of regular split monoids (this class contains all natural examples) by normal subgroups of Levi factors is given.