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- Does there exist a group isomorphism from Z to ZxZ?
Interesting way to think about it So, in general, can you never have an isomorphism from a cyclic group to a non-cyclic group of the same order?
- $\mathbb {Z} \times \mathbb {Z} $ is a PID or not? [duplicate]
we know Z is a PID but there exists no ring isomorphism between ZxZ and Z So based on this observation can we conclude that ZxZ is not a PID ? I dont think we can because if A and B are isomorphic
- Describe all group homomorphisms from Z×Z into Z
I find a similar post, which is Describe all ring homomorphisms from Z×Z into Z I also know the difference between group and ring But in this case, from ZxZ into Z, I'm so confused The textbook
- Convert from fixed axis $XYZ$ rotations to Euler $ZXZ$ rotations
Convert from fixed axis $XYZ$ rotations to Euler $ZXZ$ rotations Ask Question Asked 13 years, 8 months ago Modified 11 years, 10 months ago
- Show ZXZ lt;1,1 gt; is an infinite cyclic group. - Physics Forums
what characterize an infinite cyclic group? 1 generated by a single element 2 infinite order can you put an element canonically into a certain form? so say you have (m, n), what can I write it as?
- What is the range of the function g: ZxZ -- gt; ZxZ given by g (m,n)= (m-n . . .
Both i and ii are required to conclude that C=range (f) Homework Equations none The Attempt at a Solution I am think that the range is all integers from -infinity to +infinity I know that: * ZxZ denotes a set of ordered pairs * m,n exist in Z * range (g) exists in Z I don't know where to go with this!
- Lets help people deal with ZXZ ZXZ : r osugame - Reddit
Let's help people deal with ZXZ ZXZ well lately I've been seeing more and more players complaining about: 1 "I start triples with the same finger" 2 "triple in the middle of the jump section ruins my day" 3 "I quickly lose stamina on retina-like map"
- What are the conjugacy classes of subgroups of Z X Z?
The ladder three categories should be distinct because S1 X S1 has fund group ZXZ, S1 X R is homotopic to S1 (because R is contractible), while R X R has trivial fundamental group - so neither three of these representative are homeomorphic as none are homotopic So we have 3 distinct "isomorphism groups" of covering spaces of the torus Right?
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