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This book introduces the subject of the growth of groups from scratch, starting with basic definitions and culminating in the seminal results of Gromov and Grigorchuk and more. It is valuable reading for researchers from graduate students up who want to be acquainted with contemporary group theory.
Growth Groups is a 10 week practical, 'hands-on' training program to develop effective small group ('Growth Group') leaders. A training program useful for all Christian ministry, not just Growth Groups, because it deals with the fundamentals of gospel work.
This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one. This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory.
Like nothing else, small groups have the power to change lives. They are the ideal route to discipleship—a place where the rubber of biblical truth meets the road of human relationships. However, church leaders often feel at a loss when it comes to assessing the strengths and weaknesses of group life in a church, and they struggle with understanding and solving the root causes of problems. Group Life resources provide, in ebook format, the practical tools and training resources needed to develop life-changing small group leaders, coaches to shepherd group leaders, and ultimately, a thriving church-wide small group ministry. These resources include the updated and revised versions of the best-selling Leading Life-Changing Small Groups and Coaching Life-Changing Small Group Leaders, the new Building a Life-Changing Small Group Ministry and the supplemental Group Life Training DVD. Appropriate for individual or group study, the books function as manuals and workbooks that teach and allow readers to process and record information as they learn. Downloadable web-based vision clips and supplemental videos in the DVD help readers explore and discuss topics further. Group Life Resources conveniently integrate with the ReGroupTM curriculum, giving trainers the option to use them together. Bill Donahue and Russ Robinson’s Building a Life-Changing Small Group Ministry presents a broad introduction for pastors and point leaders to use as they navigate through the process of establish-ing and developing independent groups or a church-wide ministry of small groups.
Church leaders want to know how to make their small groups work. Drawing from the startling success of small groups at The Journey Church, Nelson Searcy and Kerrick Thomas debunk the myths, set the record straight, and show how church leaders can implement a healthy small group ministry that gets the maximum number of people involved and solves many of the important problems facing churches of all sizes. These practical strategies will produce life-changing results.
Small groups are a great way to promote the spiritual formation of church attendees. But leading them well can be hard work, especially if you don't have a plan. This practical resource helps pastors and small group point people develop and implement a 12- to 18-month strategic plan for their ministries in order to keep it healthy and growing. Developed at Saddleback Church, this completely customizable plan works for any church size and any denomination. Readers answer 22 questions that help them understand their vision, the purpose of their ministry, and how to connect members, grow numerically and spiritually, measure progress, develop leaders, create opportunities to serve, and much more. By the time they're done, readers will have developed their own personalized planner for the next year to 18 months so that they can feel prepared, confident, and purposeful about their small group ministry.