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### Questions (5)

 6 How to prove that if $\#A = n$, then $\#A^{k} = n^{k}$? And what about the formula $\frac{n!}{(n-k)!}$? 6 For $|G|$ even, $\forall x\in G\exists b\in G\setminus{\{x^{-1}\}}$ such that $bxb = x^{-1}$ 3 Being $|G| = 20$ and $H$ and $K$ subgroups of $G$ whose order is 5, prove that $K = H$ 3 If $G$ is a non-trivial group in which every non-identity element has order $2$, then $|G|$ is even 2 What happens when the order of two finite subgroups are relatively prime?

### Reputation (121)

 +10 Finite Index of Subgroup of Subgroup +5 For $|G|$ even, $\forall x\in G\exists b\in G\setminus{\{x^{-1}\}}$ such that $bxb = x^{-1}$ +10 What happens when the order of two finite subgroups are relatively prime? +5 Being $|G| = 20$ and $H$ and $K$ subgroups of $G$ whose order is 5, prove that $K = H$

 1 Finite Index of Subgroup of Subgroup

### Tags (4)

 1 group-theory × 5 0 elementary-set-theory 0 abstract-algebra × 2 0 combinatorics

### Account (1)

 Mathematics 121 rep 6