Let Fn be a free group of rank n. (a) Show that Fn contains a subgroup...

Question

Question

Let Fn be a free group of rank n. (a) Show that Fn contains a subgroup isomorphic to Fk whenever 1 <k <n. (b) Show that F2 co

Answer 1

Answer #1

No,An infinite group can not be generated by 2 elements of finite order

If an element is of finite order then it generate finite elemtents as its order is finite.

let a and b two element of finite order then their order of ab is also finite and order of any power of a is also finite.Same for as b.

Answer 2

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