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pro vyhledávání: '"Bächle, Andreas"'
The Gruenberg-Kegel graph of a group is the undirected graph whose vertices are those primes which occur as the order of an element of the group, and distinct vertices $p$, $q$ are joined by an edge whenever the group has an element of order $pq$. It
Externí odkaz:
http://arxiv.org/abs/2112.08188
Autor:
Bächle, Andreas, Margolis, Leo
In this article, we review the proofs of the first Zassenhaus Conjecture on conjugacy of torsion units in integral group rings for the alternating groups of degree 5 and 6, by Luthar-Passi and Hertweck. We describe how the study of these examples led
Externí odkaz:
http://arxiv.org/abs/2006.09031
Publikováno v:
Pacific J. Math. 312 (2021) 309-334
For a finite group $G$ and $U: = U(\mathbb{Z}G)$, the group of units of the integral group ring of $G$, we study the implications of the structure of $G$ on the abelianization $U/U'$ of $U$. We pose questions on the connections between the exponent o
Externí odkaz:
http://arxiv.org/abs/2004.03173
Autor:
Bächle, Andreas
Publikováno v:
Advances in Group Theory and Applications, Volume 8, December 2019, ADV Perspectives in Group Theory - an open space, 8B, pp157-160
This short note collects three open questions on cut groups (a class of groups generalizing rational groups).
Comment: [v2] 2 pages. This is an update compared to the published version. References and a result of N. Grittini updated. The rest re
Comment: [v2] 2 pages. This is an update compared to the published version. References and a result of N. Grittini updated. The rest re
Externí odkaz:
http://arxiv.org/abs/2001.02637
Autor:
Bächle, Andreas, Sambale, Benjamin
Publikováno v:
Monatsh. Math. 191, 665-678 (2020)
Let $K:=\mathbb{Q}(G)$ be the number field generated by the complex character values of a finite group $G$. Let $\mathbb{Z}_K$ be the ring of integers of $K$. In this paper we investigate the suborder $\mathbb{Z}[G]$ of $\mathbb{Z}_K$ generated by th
Externí odkaz:
http://arxiv.org/abs/1910.00209
Let $G$ be a finite group and $\mathcal{U} (\mathbb{Z} G)$ the unit group of the integral group ring $\mathbb{Z} G$. We prove a unit theorem, namely a characterization of when $\mathcal{U}(\mathbb{Z}G)$ satisfies Kazhdan's property $(\operatorname{T}
Externí odkaz:
http://arxiv.org/abs/1811.12184
We show that $\mathcal{U}(\mathbb{Z}G)$, the unit group of the integral group ring $\mathbb{Z} G$, either satisfies Kazhdan's property (T) or is, up to commensurability, a non-trivial amalgamated product, in case $G$ is a finite group satisfying some
Externí odkaz:
http://arxiv.org/abs/1811.12226
Autor:
Bächle, Andreas, Margolis, Leo
Publikováno v:
Proc. Amer. Math. Soc., 147(10):4221-4231, 2019
We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so does G, for
Externí odkaz:
http://arxiv.org/abs/1808.07820
Publikováno v:
Journal of Group Theory, 24(6), 1163-1188, 2021
The aim of this article is to explore global and local properties of finite groups whose integral group rings have only trivial central units, so-called cut groups. For such a group we study actions of Galois groups on its character table and show th
Externí odkaz:
http://arxiv.org/abs/1808.03546
In this paper we study the behavior of the first Zassenhaus conjecture (ZC1) under direct products as well as the General Bovdi Problem (Gen-BP) which turns out to be a slightly weaker variant of (ZC1). Among others we prove that (Gen-BP) holds for S
Externí odkaz:
http://arxiv.org/abs/1801.09422