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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
(Continued )
All that is left to prove is that μ is compatible with the operations in the two groups, that is, given m
and n in ,isμðm + nÞ= μðmÞ μðnÞ? Use the definition of μ and the properties of addition of matrices to
check this equality:
μðm + nÞ=
m + n 0
0 m + n

=
m 0
0 m

+
n 0
0 n

= μðmÞ μðnÞ:
Thus the two groups are isomorphic.
Exercises
35. Prove that the groups ð
2
, +
2
Þ, and ð
3
, ×
3
Þ are isomorphic.
36. Let (A, )and(B, ) be two isomorphic groups. Prove that (A, ) is abelian if and only if ( B, )is
abelian.
37. In Example 4 .4.29 you can read the following statements: There are many (720 = 6!) bijective
functions between the sets P
3
and ...
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Publisher Resources

ISBN: 9780123822178