GATE | GATE CS 1999 | Question 52

[5 Marks question]

Let G be a finite group and H be a subgroup of G. For a∈G, define  aH= { ah | h∈H }

a.  Show that |aH| – |H|

b.  Show that for every pair of elements a, bG, either aH=bH or aH and bH are disjoint.

c.  Use the above to argue that the order of H must divide the order of G.



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