Hi everyone;(adsbygoogle = window.adsbygoogle || []).push({});

There are some questions which are frizzling my mind, if anybody could help then plz reply to these ques which are as follows.

Q1) Prove that homomorphic image of cyclic group is itself cyclic?

Q2) Prove that any group 'G' can be embedded in a group of bijective mapping of a certain set? ( Here bijective mapping is that which is one-to-one as well as onto i.e. injective and surjective both).

Q3) Prove that the number of elements in a conjugacy class Ca of an element 'a' in a group 'G' is equal to the index of its normalizer?

If anyone has an idea about any of the above proofs then plz let me know, I hope u guys will give me this favor.

Bye

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# Homework Help: Few problems related to abstract algebra

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