{"product_id":"subgroup-growth-9783034898461","title":"Subgroup Growth","description":"\u003cp\u003e • Author(s): Alexander Lubotzky\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Group Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eSubgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged.\u003c\/p\u003e \u003cp\u003eAs well as determining the range of possible \"growth types\", for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. For example the so-called PSG Theorem, proved in Chapter 5, characterizes the groups of \u003cem\u003epolynomial subgroup growth\u003c\/em\u003e as those which are \u003cem\u003evirtually soluble of finite rank\u003c\/em\u003e. A key element in the proof is the growth of \u003cem\u003econgruence subgroups\u003c\/em\u003e in arithmetic groups, a new kind of \"non-commutative arithmetic\", with applications to the study of lattices in Lie groups. Another kind of non-commutative arithmetic arises with the introduction of \u003cem\u003esubgroup-counting zeta functions\u003c\/em\u003e; these fascinating and mysterious zeta functions have remarkable applications both to the \"arithmetic of subgroup growth\" and to the classification of finite p-groups.\u003c\/p\u003e \u003cp\u003eA wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and strong approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained \"windows\", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274965770391,"sku":"9783034898461","price":4040.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783034898461.webp?v=1769281478","url":"https:\/\/atlanticbooks.com\/products\/subgroup-growth-9783034898461","provider":"Atlantic Books","version":"1.0","type":"link"}