### Questions (9)

 3 What is the difference between cyclic groups and periodic groups? 2 Reasons behind the analogy between “order of groups” and “sets” (if it exists). 2 Prove $\liminf \left(\frac{n!}{(n-k)! n^k}\right) = 1,\ k =$ constant. 1 Prove $H\circ N = H\cap N$. Where $H$ and $N$ are two subgroups of a group $G$. [closed] 0 Let G be a group, and $N\triangleleft G$. Then, the quotient map $q: G\rightarrow G/N$ given by $q(g) = g\circ N$ is an epimorphism.

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 1 Prove $H\circ N = H\cap N$. Where $H$ and $N$ are two subgroups of a group $G$. 1 Difference between one to one function and one to one correspondence 0 Is $N$ normal to $HN$ if $H$ subgroup and $N$ normal subgroup of the group $G$

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 1 group-theory × 10 0 binomial-distribution 1 functions 0 limits 0 number-theory × 6 0 permutations 0 abstract-algebra × 4 0 probability-theory 0 group-isomorphism × 2 0 poisson-distribution

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