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Results tagged with gr.group-theory
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user 2024
Questions about the branch of algebra that deals with groups.
3
votes
Algebraic integers on the unit circle
The question is a bit ambiguous because "lie on the unit circle" is ambiguous. A closely worded question is:
Let $S$ be a set of archimedean places of a number field $K$. What is the subgroup $K_S …
- 4,593
2
votes
Accepted
on the computation of decomposition groups
Henri Cohen's A Course in Computational Algebraic Number Theory contains quite a bit of information. Chapters 4.8, 6.2 and 6.3 combined result in algorithms that compute decomposition groups. Note tha …
- 4,593
6
votes
Navigating $\mathbb{Z}/p\mathbb{Z}$
Let $r$ be the "base" and $x$ the number to represent.
Let $m = \log_{2} (p) + \epsilon$. Construct the matrix $L$:
$$\begin{pmatrix}
x & \lambda & 0 & & ... & & 0 \\\\
1 & 0 & \lambda & & & & 0 \\\ …
- 4,593
2
votes
Analog to the Chinese Remainder Theorem in groups other than Z_n.
I did a course titled something similar in my undergraduate, and while it didn't teach the following applications, H. Cohen's A Course in Computational Algebraic Number Theory (which I read right afte …
- 4,593