Complete the group as isomorphic

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Homework Help Overview

The discussion revolves around completing multiplication tables for groups, specifically focusing on constructing a group that is isomorphic to Z4 and another that is not isomorphic to Z4. The subject area involves group theory in abstract algebra.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants share their attempts at filling out the multiplication tables for both groups, with some questioning the validity of certain tables based on group properties. There are discussions about the implications of having all elements equal in a table and the requirements for group structure.

Discussion Status

The conversation includes various attempts at constructing the required groups, with some participants expressing doubts about the correctness of certain tables. There is a mix of agreement on the correct forms of the tables, but no explicit consensus is reached on the final answers.

Contextual Notes

Participants mention the importance of adhering to group properties, and there are reminders about not providing complete answers in the homework section, indicating a focus on learning through discussion rather than direct solutions.

Anarchy6k2
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1. Complete the following table to obtain a Group, G, that is isomorphic to Z4
2. Complete the same table to obtain a Group, H, that is NOT isomorphic to Z4

*| a b c d
a|
b|
c|
d|


I tried to complete the group as isomorphic, can anyone tell me if this is correct?

*| a b c d
a| a a a a
b| a b c d
c| a c a c
d| a d c b

And here is my attempt at part to as if it is not an isomorphism


*| a b c d
a| a b c d
b| b c d a
c| c d a b
d| d a b c
 
Last edited:
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Anarchy6k2 said:

*| a b c d
a| a a a a
b| a a a a
c| a a a a
d| a a a a
You're saying that this is the multiplication table for a group? What's the inverse of b?
 
:(

All I can say is LOL you might want to work on the table with all a's in it. It has to follow group properties. I hope that's not the grade you want in this class.
 
ok here

ok now that you got rid of all those crazy a's here is what I got.

Part 1. isomorphic to Z4
abcd
bcda
cdab
dabc

part 2. not isomorphic to Z4
abcd
badc
cdab
dcba

Anyone else get this?
 
Thanks, I was talking it over with some friends and we all got the same thing. Thanks for the assistance haha now I can definatly get an A ^_^
 
Yes, all groups of order 4 are either isomorphic to Z4 or the Klein 4 group.

CrazyCalcGirl- please do NOT give complete answers in the homework section.
 

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