Let H and K be a subgroups of a group G. Define the relation as follows: a ~ b if and only if a = hbk, for some h E H and kEK Prove that 2 2 is an equivalence relation on G. on G
Let H and K be a subgroups of a group G. Define the relation as follows: a ~ b if and only if a = hbk, for some h E H and kEK Prove that 2 2 is an equivalence relation on G. on G
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let H and K be a subgroups of a group G. Define the relation ~ on G
as follows:
a
b if and only if a = hbk, for some h E H and k E K
Prove that ~ is an equivalence relation on G.
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