Aakash Singh Bais

### Questions (10)

 3 What is the difference between cyclic groups and periodic groups? 2 Suppose that $G$ is a group and $H$ a nonempty finite sub- set of $G$ closed under the product in $G$. Then $H$ is a subgroup of $G$. 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]

### Reputation (100)

 +10 Suppose that $G$ is a group and $H$ a nonempty finite sub- set of $G$ closed under the product in $G$. Then $H$ is a subgroup of $G$. +5 Prove $H\circ N = H\cap N$. Where $H$ and $N$ are two subgroups of a group $G$. +10 Prove $H\circ N = H\cap N$. Where $H$ and $N$ are two subgroups of a group $G$. +5 Reasons behind the analogy between “order of groups” and “sets” (if it exists).

 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 $G$

### Tags (13)

 1 group-theory × 11 0 group-isomorphism × 2 1 functions 0 binomial-distribution 0 number-theory × 6 0 limits 0 abstract-algebra × 5 0 permutations 0 proof-explanation × 2 0 probability-theory

### Accounts (8)

 Mathematics 100 rep 99 bronze badges Chemistry 68 rep 66 bronze badges Psychology & Neuroscience 26 rep 55 bronze badges Biology 3 rep 22 bronze badges Meta Stack Exchange 1 rep 11 bronze badge