1. Let G with a binary operation * be a group. Now, choose one element g ∈ G and define new
binary operation # in G as follow : a # b = a * g * b.
Check whether ( G, #) form a group or not.
2. Determine all subgroup of![](https://3.bp.blogspot.com/-KoDIPyY9KeE/Vul52fxSnJI/AAAAAAAByXE/q9chyFuvJtsNRr0nRwmegyMQR4IDZ8ltg/s1600/z.jpg)
3. Find the number of generator of cyclic group![](https://3.bp.blogspot.com/-4IgfzcP7sYo/Vul6MhOt32I/AAAAAAAByXM/A4nOFIIUfHgdyTomtDCNc0kJDnVKfUkCA/s400/z.jpg)
4. Let G be a group and g ∈ G. A function f : G → G is defined by
that f is an automorphism.
binary operation # in G as follow : a # b = a * g * b.
Check whether ( G, #) form a group or not.
2. Determine all subgroup of
![](https://3.bp.blogspot.com/-KoDIPyY9KeE/Vul52fxSnJI/AAAAAAAByXE/q9chyFuvJtsNRr0nRwmegyMQR4IDZ8ltg/s1600/z.jpg)
3. Find the number of generator of cyclic group
![](https://3.bp.blogspot.com/-4IgfzcP7sYo/Vul6MhOt32I/AAAAAAAByXM/A4nOFIIUfHgdyTomtDCNc0kJDnVKfUkCA/s400/z.jpg)
4. Let G be a group and g ∈ G. A function f : G → G is defined by
![](https://3.bp.blogspot.com/-8xvCSz6hxJw/Vul6YDvvv_I/AAAAAAAByXU/rq_btdF7j3IE1KXMag1Cjv9rgJGuZicjQ/s400/z.jpg)
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