Originally Posted by

**themanandthe** 3. prove or disprove:

a.there is no group G and a normal subgroup H of G (when H is not G or {1G}) so that G/H isomorphic to G.

b. there is no group G and subgroup H [so that H is not G] so that G

isomorphic to H.

c. for all n natural there is a group G and a subgroup H

[wich both are Independent in n] so that rank(G)=2 and rank(H)=n

d. for all G group from order n, there are no m<n (when m belongs to N)

so that there is monomorphism G->Sm.

e. for all group G , H subgroup of G so that: Z(H) is a subgroup of Z(G).