1. Construct a Cayley table for the group of symmetries of a square, write each element as a permutation. Label eachvertex of the square by the numbers 1,2,3,4 clockwise, label the upper left corner by 1. For example the 90°-rotation1 2 3should be 1). Determine, with proof, whether or not this group is abelian. Call this group D2 3 41 2 3 42. Find the subgroup of D₁, of Problem 1, generated by the element (1234) =233. Find the center of D₁.4. Find the centralizer of the element (24) =2)1 4 3 2,1 2 3 4in D₁41)and find its order.

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1. Construct a Cayley table for the group of symmetries of a square, write each element as a permutation. Label each vertex of the square by the numbers 1,2,3,4 clockwise, label the upper left corner by 1. For example the 90°-rotation should be 1 2 3 234 1). Determine, with proof, whether or not this group is abelian. Call this group D

1. Construct a Cayley table for the group of symmetries of a square, write each element as a permutation. Label each vertex of the square by the numbers 1,2,3,4 clockwise, label the upper left corner by 1. For example the 90°-rotation should be 1 2 3 234 1). Determine, with proof, whether or not this group is abelian. Call this group D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 10E: Exercises 10. Find an isomorphism from the multiplicative group to the group with multiplication...

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