Automorphisms and characterizations of finite generalized ...
Chapter 6: Isomorphisms Definition and Examples Cayley’ Theorem Automorphisms.
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Chapter 6: Isomorphisms Definition and Examples Cayley’ Theorem Automorphisms
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Transcript of Chapter 6: Isomorphisms Definition and Examples Cayley’ Theorem Automorphisms.
Example:
Find a group of permutations that is isomorphic to the group U(12)={1,5,7,11}.
Solution: Let
and the multiplication tables for both groups is given by:
},,,{)12(Then 11751 TTTTU
Example:
isomorphicnot are ,.)(R and ,.)( that Show **C
groupsboth in 1 of solutions ofnumber at theLook
:Solution4 x
Determine all automorphisms of Z_10That is, find Aut(Z_10). Show that Aut(Z_10) is a cyclic group. Moreover,
)10()( 10 UZAut