List questions from permutation-cycles

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Finding $(ab)^{-2}$ and $(a^{-1})(b^{-1})$ for $a=(236)(57), b=(147).$

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Let $H<\mathfrak S_n$ and $\sigma\in H $. Prove/disprove that every disjoint cycle in its decomposition belong to $H.$

Published on 29 Jan 2020 - 18:26

List Question

Finding the order of a permutation $\sigma$ and thus using it to find $\sigma^{122}$

Simple proof of $A_n$ being simple?

One Problem Regarding Permutation

Should cycles in direct product group be disjoint?

Why do the triangular numbers initially form long cycles mod $2^k$?

Finding $(ab)^{-2}$ and $(a^{-1})(b^{-1})$ for $a=(236)(57), b=(147).$

Sign of permutation with first all odd numbers and then even numbers

Find out number of 2-cycle permutations

Combinatorial bijection of primitive factorization

Do we need the "consecutive" term in this definition?

Explain proof for strategy to write a cycle as transpositions

element of maximal and minimal order

question about permutations with a combinatorial approach to solving

Transform a permutation from cycle notation to standard form

Let $H<\mathfrak S_n$ and $\sigma\in H $. Prove/disprove that every disjoint cycle in its decomposition belong to $H.$

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