Decide whether each of the statements is true or false. Circle your anewer You d

Question

Decide whether each of the statements is true or false. Circle your anewer You do not need to justify your answer. I and N is any subgroup of G then the set of cosets G/N is a group with operation (9?N)GN)-(01a)N. False The 2-cycles (ij) E S, with 1 S iS n and1 siS n generate the subgroup True An- True False IfGisa finite group and N is any subgroup of G then [G: N] = |G/M = then Ker( G/ Ker(p) ?(G). If ?: G-+ H is a group homomorphism, then ?(G) is a subgroup of H and ?-1 (H) is a subgroup of G. True False True False If N aK and K

Explanation / Answer

a) it is true called quotient group.

b) it is false since An is generated by 3 cycles

c) it is true called index of a subgroup.

d) it is true called fundamental theorem of homomorphism.

e) it is true

f) false since normality is not transitive

g) true by the definition of normal subgroup.

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