Classifying blocks with abelian defect groups of rank $3$ for the prime $2$ [PDF]
, 2017 In this paper we classify all blocks with defect group $C_{2^n}\times C_2\times C_2$ up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of $2$-blocks with abelian ...
Eaton, Charles, Livesey, Michael
core +5 more sources
AN EXPLICIT FORMULA FOR THE NUMBER OF SUBGROUPS OF A FINITE ABELIAN p-GROUP UP TO RANK 3 [PDF]
Communications of the Korean Mathematical Society, 2013 In this paper we give an explicit formula for the total number of subgroups of a finite abelian -group up to rank three.
Ju-Mok Oh
openaire +2 more sources
Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank [PDF]
Mathematische Nachrichten, 2023 AbstractLet X be a ‐factorial compact Kähler klt threefold admitting an action of a free abelian group G, which is of positive entropy and of maximal rank. After running the G‐equivariant log minimal model program, we show that such X is either rationally connected or bimeromorphic to a Q‐complex torus.
Guolei Zhong
openaire +4 more sources
𝑛-dimensional projective varieties with the action of an abelian group of rank 𝑛-1 [PDF]
Transactions of the American Mathematical Society, 2016 Let X X be a normal projective variety of dimension n ≥ 3 n \ge 3 admitting the action of the group G := Z ⊕ n − 1 G := \mathbb {Z}^{\oplus n-1} such that ...
De‐Qi Zhang
openaire +3 more sources
Maximal abelian subgroups of the finite symmetric group [PDF]
International Journal of Group Theory, 2021 Let $G$ be a group. For an element $a\in G$, denote by $\cs(a)$ the second centralizer of~$a$ in~$G$, which is the set of all elements $b\in G$ such that $bx=xb$ for every $x\in G$ that commutes with $a$.
Janusz Konieczny
doaj +1 more source
Compact Kähler threefolds with the action of an abelian group of maximal rank [PDF]
Proceedings of the American Mathematical Society, 2021 17 pages, Introduction reorganized, Remark 3.2 added, Proceedings of the American Mathematical Society (to appear)
openaire +3 more sources
New models for some free algebras of small ranks
Karpatsʹkì Matematičnì Publìkacìï, 2023 Dimonoids, generalized digroups and doppelsemigroups are algebras defined on a set with two binary associative operations. The notion of a dimonoid was introduced by J.-L.
A.V. Zhuchok, G.F. Pilz
doaj +1 more source
Groups of finite Morley rank with a generically multiply transitive action on an abelian group
Model Theory, 2022 We investigate the configuration where a group of finite Morley rank acts definably and generically $m$-transitively on an elementary abelian $p$-group of Morley rank $n$, where $p$ is an odd prime, and $m\geqslant n$. We conclude that $m=n$, and the action is equivalent to the natural action of $\operatorname{GL}_n(F)$ on $F^n$ for some algebraically ...
Berkman, Ayşe, Borovik, Alexandre
openaire +2 more sources
Elekes-Szabó for groups, and approximate subgroups in weak general position
Discrete Analysis, 2023 Elekes-Szabó for groups, and approximate subgroups in weak general position, Discrete Analysis 2023:6, 28 pp. An important theorem of Elekes and Szabó shows that given an algebraic relation between triples of complex numbers (such as e.g.
Martin Bays +2 more
doaj +1 more source
Dieudonné theory via cohomology of classifying stacks
Forum of Mathematics, Sigma, 2021 We prove that if G is a finite flat group scheme of p-power rank over a perfect field of characteristic p, then the second crystalline cohomology of its classifying stack $H^2_{\text {crys}}(BG)$ recovers the Dieudonné module of G.
Shubhodip Mondal
doaj +1 more source