A Permutation Group Theory Model for Analyzing Structural Dynamics in Pentecostal Congregational Growth

Abstract

This paper presents a refined mathematical framework for analyzing the structural dynamics of congregational growth, specifically within the context of Pentecostal churches, utilizing the principles of permutation group theory. We model the assignment and rotation of congregants across various ministry roles and programs as group actions on a finite set of members. By rigorously defining structural transformations as permutations, we leverage concepts such as orbits, stabilizers, and the Orbit-Stabilizer Theorem to quantify member engagement and participation stability. The model posits that optimal congregational growth is achieved through a strategic balance of rotational exposure (large orbits) and core stability (small stabilizers). A theoretical simulation demonstrates that programmatic structures designed with specific cycle decompositions—representing intentional rotation—correlate with higher average member growth rates. This algebraic approach offers church leadership a novel, mathematically informed tool for designing sustainable discipleship pathways and optimizing ministry deployment, moving beyond traditional sociological or purely organizational models.