{"product_id":"9781470453831-factorizations-of-almost-simple-gro","title":"Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eA characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these non-trivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type.\u003cbr\u003eA characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these non-trivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then applied to study s-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected 3-arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Ho?man-Singleton graph.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54845443768694,"sku":"9781470453831","price":69.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36018286.jpg?v=1757557695","url":"https:\/\/www.rarewaves.com\/products\/9781470453831-factorizations-of-almost-simple-gro","provider":"Rarewaves.com","version":"1.0","type":"link"}