GATE | GATE CS 1999 | Question 52
Last Updated :
09 Oct, 2017
[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, b∈G, 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.
Answer:
Explanation:
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