# Tagged Questions

677 views

### Is there an infinite field of characteristic 2 whose multiplicative group is torsion free and (direct-sum) indecomposable?

Let $F$ be a infinite field of characteristic 2 whose multiplicative group $F^*$ is torsion free. I would like to conclude that $F^*$ is decomposable or find an example where $F^*$ is indecomposable. ...
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### Reducing 12th degree eqns (12T179) to an 11th degree eqn

I always wondered if the fact that the quartic can be solved by a cubic can be generalized to other even degrees $n$, namely if there is an ordering of the roots $x_i$ of form ...
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### Fantastic properties of Z/2Z

Recently I gave a lecture to master's students about some nice properties of the group with two elements $\mathbb{Z}/2\mathbb{Z}$. Typically, I wanted to present simple, natural situations where the ...
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### Simple automorphism groups of field extensions of infinite transcendence degree

Let $k$ be an algebraically closed field and let $K/k$ be a field extension of infinite transcendence degree where $K$ is algebraically closed. Is it true that $\mathrm{Aut}_k(K)$ is a simple group? ...
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### The “interplay” between additive and multiplicative structure in a field

A field is an ordered triple $(F, +,\cdot)$ of a set $F$ and binary operations $+,\times$ on $F$ such that $(F,+)$ and $(F\backslash 0,\times)$ are abelian groups satisfying the distributive laws ...
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### Isomorphic general linear groups implies isomorphic fields?

Suppose $n > 1$ is a natural number. Suppose $K$ and $L$ are fields such that the general linear groups of degree $n$ over them are isomorphic, i.e., $GL(n,K) \cong GL(n,L)$ as groups. Is it ...
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### Heisenberg-type groups over rings with involution

Hello everyone! In a paper "Coverings of twisted Chevalley groups over commutative rings" Eiichi Abe intoroduced the following construction: Let $R$ be a commutative ring and $x\mapsto\overline{x}$ ...
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### torsion group of the multiplicative group of a field

Let $F$ be any field of zero characteristic, $F^{\ast}$ its multiplicative group and $T$ is the torsion group. Is it true that $T$ is a direct summand for $F^{\ast}$?
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### Orders of field automorphisms of algebraic complex numbers

Let $Aut(\bar{Q})$ be the automorphism group on the field of algebraic complex numbers. The order of an element $f \in Aut(\bar{Q})$ is the least natural number $n$ (if there exists one) such that ...
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### Which commutative groups are the group of units of some field?

Inspired by a recent question on the multiplicative group of fields. Necessary conditions include that there are at most $n$ solutions to $x^n = 1$ in such a group and that any finite subgroup is ...
We know the following isomorphism theorem for fields: Let $F, F'$ be fields. Suppose $E$ is an extension field of $F$ and $\overline{F}$ is the algebraic closure of $F$. Also $\overline{F'}$ is the ...
This is sort of a random, spur of the moment question, but here goes: We define [with apologies to Conan the Barbarian] a field K to be $\textbf{Kummerian}$ if there exists an index set I, and ...