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Questions about the branch of algebra that deals with groups.
0
votes
Accepted
Same rational points
No: Take $k$ to be the rational numbers and $G$ to be the group of third roots of unity. Then the only rational point in $G$ is $1$. Then take $H$ to be the component of the identity. This satisfies y …
3
votes
Accepted
Does viewing multiplicative functions as morphisms from $\mathbb{Q}^*\to\mathbb{C}^*$ have a...
Actually number theorists more-or-less do the exact opposite of what you suggest.
Namely, as explained in the comments, a multiplicative function is determined by its values on the primes. This sugges …
11
votes
Which groups are Galois over some p-adic field?
I'll upgrade my comment to an answer.
Any finite Galois extension of $\mathbb{Q}_l$ of degree coprime to $l$ is tamely ramified. In particular, its Galois group is an extension of two cyclic groups. …
3
votes
Accepted
Understanding the structure of unitary groups
As you already seem to know, unitary groups are classified by separable quadratic field extensions (in fact one should really work with separable quadratic algebras, i.e. also $F\times F$, correspondi …