(i) Let G be a non-cyclic group of order 8 with a cyclic subgroup K of...

 

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(i) Let G be a non-cyclic group of order 8 with a cyclic subgroup K of order 4. Show that if G splits over K then G is isomorphic to either C₂ x C4 or Dg, while if G does not split over K then GQ8. (ii) Hence show that v(8) = 5. (i) Let G be a non-cyclic group of order 8 with a cyclic subgroup K of order 4. Show that if G splits over K then G is isomorphic to either C₂ x C4 or Dg, while if G does not split over K then GQ8. (ii) Hence show that v(8) = 5.

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0 M let G be a noncyclic group of order which is grou... View the full answer