Suppose G is a group, H a subgroup of G, and a and b elements of G. If a in bH then b in aH.

Harlen Pritchard 2020-12-15 Answered

Suppose G is a group, H a subgroup of G, and a and b elements of G. If abH then baH.

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Expert Answer

opsadnojD
Answered 2020-12-16 Author has 95 answers

Suppose
aHbH
Let xaHbH, then there exist h1,h2H
Such that,
x=ah1andx=bh2
a=xh11andb=xh21
a=bh2h11
aH=bh2h11H=bH
(since aH=HifaH)
Now, if abH, using above theorem
Since bbH, then aH=bHbaH
aHandaaHaaHbH
aHbH0
So aHbH=0
baH
Hence G be a group, H a subgroup of G, and a and b elements of G. If abH then baH.

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