equal
deleted
inserted
replaced
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 |