{"product_id":"ordered-permutation-groups-paperback-9780521241908","title":"Ordered Permutation Groups (Paperback) 9780521241908","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eOrdered Permutation Groups\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAs a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eA. M. W. Glass (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521241908, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 7 January 1982\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e332 pages\u003cbr\u003e22.8 x 15.2 x 1.9 cm, 0.499 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAs a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Opening the innings: 1. Introduction\u003cbr\u003e 2. Doubly Transitive A\u003cbr\u003e Part II. The structure theory: 3. Congruences and blocks\u003cbr\u003e 4. Primitive ordered permutation groups\u003cbr\u003e 5. The wreath product\u003cbr\u003e Part III. Applications to ordered permutation groups: 6. Simple-permutation groups\u003cbr\u003e 7. Uniqueness of representation\u003cbr\u003e 8. Pointwise suprema and closed subgroups\u003cbr\u003e Part IV. Applications to lattice-ordered groups: 10. Embedding theorums for lattice-ordered groups\u003cbr\u003e 11. Normal valued lattice-ordered groups\u003cbr\u003e Part V. The author's perogative: 12. Algebraically closed lattice-ordered groups\u003cbr\u003e 13. The word problem for lattice-ordered groups.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005373206808,"sku":"9780521241908","price":68.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521241908i_3d1bd25c-a230-4012-8285-3b79dc8ad5eb.jpg?v=1691374065","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/ordered-permutation-groups-paperback-9780521241908","provider":"Freshly Printed Books","version":"1.0","type":"link"}