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Results tagged with gr.group-theory
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user 13025
Questions about the branch of algebra that deals with groups.
13
votes
1
answer
2k
views
A map from the coinvariants of the dual to the dual of the invariants for a G-module
Suppose $G$ is a group and $X$ is a $\mathbb{Z}[G]$-module. Recall that the augmentation ideal $I \subset \mathbb{Z}[G]$ is generated by elements of the form $g - 1$ for $g \in G$, the coinvariants a …
- 506
11
votes
Accepted
Conjugacy in $GL(n,\mathbb Z)$
The Conjugacy Problem in $\operatorname{GL}(n, \mathbb{Z})$ by Eick, Hofmann and O'Brien gives an algorithm for solving this problem, which has been implemented in Magma.
- 506
5
votes
A map from the coinvariants of the dual to the dual of the invariants for a G-module
I will answer the question in the case that $G$ is cyclic or pro-cyclic. Write $t$ for a (topological) generator of $G$. Then we can describe $X^G$ and $X_G$ as the kernel and cokernel of $t-1$:
$$
…
- 506