Exercise 7.6. Show that each row and column of the group table contains all of the elements of G exactly once. Use this to show that there if |G| = 2 or 3, then there is only one possible group table. Later we can use this to deduce that there is exactly one group of order 2 and one group of order 3 up to isomorphism.
Exercise 7.6. Show that each row and column of the group table contains all of the elements of G exactly once. Use this to show that there if |G| = 2 or 3, then there is only one possible group table. Later we can use this to deduce that there is exactly one group of order 2 and one group of order 3 up to isomorphism.
Advanced Engineering Mathematics
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This is group theory question, please explain it using simple words step by step, thanks :)
Transcribed Image Text:Exercise 7.6. Show that each row and column of the group table contains all of the
elements of G exactly once.
Use this to show that there if |G| = 2 or 3, then there is only one possible group table.
Later we can use this to deduce that there is exactly one group of order 2 and one
group of order 3 up to isomorphism.
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VIEWStep 2: Proof of the statement "Each element of G appears exactly once in each row and each column".
VIEWStep 3: Proof of the fact "There is only one possible group table if |G|= 2 or 3".
VIEWStep 4: Proof of "There is exactly one group of order 2 and one group of order 3 up to isomorphism".
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