- 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?
- 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
- Describe all ring homomorphisms - Mathematics Stack Exchange
Describe all ring homomorphisms of: a) $\\mathbb{Z}$ into $\\mathbb{Z}$ b) $\\mathbb{Z}$ into $\\mathbb{Z} \\times \\mathbb{Z}$ c) $\\mathbb{Z} \\times \\mathbb{Z
- Show that $Z\times Z$ is not cyclic. . . [duplicate]
Recall that an infinite cyclic group is isomorphic to $\mathbb {Z}$ We wish to show that we do not have an isomorphism between $\mathbb {ZxZ\;and\;Z}$ Note that $\mathbb {ZxZ}$ is an infinite group (under addition of course) Now, in order for there to even be potential for an isomorphism, two spaces must have equal dimension
- $\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
- Cardan angle (zxz, zxzxz) rotation - Mathematics Stack Exchange
On the wikipedia page there is a listing of 12 matrices that can be used to represent a yaw-pitch-roll rotation series (YXZ) as a ZXZ rotation, or an XZX rotation, or an XZY rotation 1) Should t
- Presentation $\langle x,y,z\mid xyx^ {-1}y^ {-2},yzy^ {-1}z^ {-2},zxz . . .
This is a very well-known presentation of the trivial group, to be compared with the presentation of Higman's infinite group with no finite quotient I do not know of any easy proof The proof I'm going to give is due to Bernhard Neumann in An Essay on Free Products of Groups with Amalgamations (Philosophical Transactions of the Royal Society of London, Series A, 246, 919 (1954), pp 503-554
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