The Sylow $p$-subgroups of the finite simple groups
In this short article, we give a summary of the Sylow $p$-subgroups of the finite simple groups of classical Lie type.
math.GR↗
arXiv subjects
Hannah Knight
Publications and source records attributed to Hannah Knight.
The essential $2$-dimension of the linear groups
In this paper, we compute the essential $2$-dimension when the defining prime is odd of the general linear groups, the projective general linear groups, the special linear groups when $n$ is odd or $n = 2$, as well as the special linear groups and quotients of it (such as the projective special linear groups) in the case case $q \equiv 1 \mod 4$, $s = v_2(q-1)$, and $\Gamma = \text{Gal}(k(\zeta_{2^s})/k)$ is trivial.
math.GR↗
The essential $l$-dimension of finite groups of Lie type, $l \neq 2$
In this paper, we compute the essential $l$-dimension of the finite groups of classical Lie type for odd primes $l$ not equal to the defining prime, specifically the general linear groups, the symplectic groups, the orthogonal groups, and the unitary groups, and the simple factors in their Jordan-H\"older series.
math.GR↗
The essential p-dimension of the split finite quasi-simple groups of classical Lie type
In this paper, we compute the essential $p$-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the symplectic groups, and the orthogonal groups.
math.GR↗
Translation of Tschebotarow's "The Problem of Resolvents and Critical Manifolds"
This is an English translation of "The Problem of Resolvents and Critical Manifolds" by Tschebotarow/Chebotarev. In this article, Chebotarev explains his work on resolvent problems using critical manifolds. The current ideas of resolvent degree and essential dimension arose out of the resolvent problems Chebotarev addresses here. Original abstract by Chebotarev: "This paper is devoted to the study of the problem of resolvents, i.e., the problem of finding the resolvent by a given equation, whose coefficients depend on several independent parameters, the number of parameters in the coefficients being as small as possible. The author connects the problem to the study of critical manifolds in the space of equation parameters."
math.HO↗
Translation of Tschebotarow's "The Resolvent Problem"
This is an English translation of "The Resolvent Problem" by Tschebotarow/Chebotarev. In this article, Chebotarev summarizes the history of the resolvent problem from compass and ruler constructions to Klein and Hilbert' formlutions of the problems. He also describes his work on the problem up until that time. The ideas of resolvent degree and essential dimension arose out of the resolvent problems Chebotarev describes here.
math.HO↗