Monocarpy versus polycarpy is one of the fundamental developmental dichotomies in flowering plants. Advances in the understanding of the genetic basis of this dichotomy are important for basic biological reasons and practically for genetic manipulation of growth development in economically important plants. Nine wheat introgression lines (ILs) harboring germplasm of the Lophopyrum elongatum genome present in the octoploid amphiploid Triticum aestivum cv. Chinese Spring (subgenomes AABBDD) × L. elongatum (genomes EE) were selected from a population of ILs developed earlier. These ILs were employed here in genomic analyses of post-sexual cycle regrowth (PSCR), which is a component of polycarpy in caespitose L. elongatum. Analyses of disomic substitution (DS) lines confirmed that L. elongatum chromosome 4E confers PSCR on wheat. The gene was mapped into a short distal region of L. elongatum arm 4ES and was tentatively named Pscr1. ILs harboring recombined chromosomes with 4ES segments, including Pscr1, incorporated into the distal part of the 4DS chromosome arm were identified. Based on the location, Pscr1 is not orthologous with the rice rhizome-development gene Rhz2 located on rice chromosome Os3, which is homoeologous with chromosome 4E, but it may correspond to the Teosinte branched1 (TB1) gene, which is located in the introgressed region in the L. elongatum and Ae. tauschii genomes. A hexaploid IL harboring a large portion of the E-genome but devoid of chromosome 4E also expressed PSCR, which provided evidence that perennial growth is controlled by genes on other L. elongatum chromosomes in addition to 4E.