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pro vyhledávání: '"BUSH, MICHAEL R."'
Autor:
Boston, Nigel, Bush, Michael R.
We consider the Galois group $G_2(K)$ of the maximal unramified $2$-extension of $K$ where $K/\mathbb{Q}$ is cyclic of degree $3$. We also consider the group $G^+_2(K)$ where ramification is allowed at infinity. In the spirit of the Cohen-Lenstra heu
Externí odkaz:
http://arxiv.org/abs/2012.14824
Autor:
Bush, Michael R.
A characterization of the quotients of $p$-class tower groups of quadratic fields by terms in the lower $p$-central series plays an important role in the formulation of conjectures by Boston, Hajir and the author about the distribution of such groups
Externí odkaz:
http://arxiv.org/abs/2001.01396
Autor:
Bush, Michael R., Quijada, Danjoseph
Publikováno v:
Involve 14 (2021) 361-376
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over $\mathbb{F}_q$ ge
Externí odkaz:
http://arxiv.org/abs/1805.03238
Let $p$ be an odd prime. For a number field $K$, we let $K_\infty$ be the maximal unramified pro-$p$ extension of $K$; we call the group $\mathrm{Gal}(K_\infty/K)$ the $p$-class tower group of $K$. In a previous work, as a non-abelian generalization
Externí odkaz:
http://arxiv.org/abs/1803.04047
We prove that the arboreal Galois representations attached to certain unicritical polynomials have finite index in an infinite wreath product of cyclic groups, and we prove surjectivity for some small degree examples, including a new family of quadra
Externí odkaz:
http://arxiv.org/abs/1608.03328
Autor:
Bush, Michael R.
Despite robust scholarship on the general themes of state-building, little scholarship exists on the strategies of exogenous powers on the construction of developing states. Further complicating these strategies is the influence of strong men, local
Externí odkaz:
http://hdl.handle.net/10945/27803
Autor:
Bush, MIchael R., Mayer, Daniel C.
The $p$-group generation algorithm is used to verify that the Hilbert $3$-class field tower has length $3$ for certain imaginary quadratic fields $K$ with $3$-class group $\mathrm{Cl}_3(K) \cong [3,3]$. Our results provide the first examples of finit
Externí odkaz:
http://arxiv.org/abs/1312.0251
Cohen and Lenstra have given a heuristic which, for a fixed odd prime $p$, leads to many interesting predictions about the distribution of $p$-class groups of imaginary quadratic fields. We extend the Cohen-Lenstra heuristic to a non-abelian setting
Externí odkaz:
http://arxiv.org/abs/1111.4679
Akademický článek
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Autor:
Bush, Michael R., Labute, John
Let p be an odd prime and S a finite set of primes = 1 mod p. We give an effective criterion for determining when the Galois group G=G_S(p) of the maximal p-extension of Q unramified outside of S is mild when |S|=4 and the cup product H^1(G,Z/pZ) \ot
Externí odkaz:
http://arxiv.org/abs/math/0602189