src/HOL/Algebra/Sym_Groups.thy
changeset 69597 ff784d5a5bfb
parent 69122 1b5178abaf97
child 73477 1d8a79aa2a99
equal deleted inserted replaced
69596:c8a2755bf220 69597:ff784d5a5bfb
   315 qed
   315 qed
   316 
   316 
   317 
   317 
   318 subsection \<open>Unsolvability of Symmetric Groups\<close>
   318 subsection \<open>Unsolvability of Symmetric Groups\<close>
   319 
   319 
   320 text \<open>We show that symmetric groups (@{term\<open>sym_group n\<close>}) are unsolvable for @{term\<open>n \<ge> 5\<close>}.\<close>
   320 text \<open>We show that symmetric groups (\<^term>\<open>sym_group n\<close>) are unsolvable for \<^term>\<open>n \<ge> 5\<close>.\<close>
   321 
   321 
   322 abbreviation three_cycles :: "nat \<Rightarrow> (nat \<Rightarrow> nat) set"
   322 abbreviation three_cycles :: "nat \<Rightarrow> (nat \<Rightarrow> nat) set"
   323   where "three_cycles n \<equiv>
   323   where "three_cycles n \<equiv>
   324            { cycle_of_list cs | cs. cycle cs \<and> length cs = 3 \<and> set cs \<subseteq> {1..n} }"
   324            { cycle_of_list cs | cs. cycle cs \<and> length cs = 3 \<and> set cs \<subseteq> {1..n} }"
   325 
   325