Consider two groups, G 1 and G 2 . Group G 1 is defined as {1,a,a^2 ,a^3 } with operation ⋅ ⋅ such that a^4 =1, and group G2 is defined as {1,b,b^2 ,b^3 } with operation ∗ such that b^4 =1. Determine whether the two groups G 1 and G 2 are isomorphic. If they are, find an isomorphism between them.

Consider two groups, G 1 and G 2 . Group G 1 is defined as {1,a,a^2 ,a^3 } with operation ⋅ ⋅ such that a^4 =1, and group G2 is defined as {1,b,b^2 ,b^3 } with operation ∗ such that b^4 =1. Determine whether the two groups G 1 and G 2 are isomorphic. If they are, find an isomorphism between them.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 24E: Find two groups of order 6 that are not isomorphic.

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