Results 61 to 70 of about 301 (136)
Recognizing powers in nilpotent groups and nilpotent images of free groups [PDF]
Journal of the Australian Mathematical Society, 2007 AbstractAn element in a free group is a proper power if and only if it is a proper power in every nilpotent factor group. Moreover there is an algorithm to decide if an element in a finitely generated torsion-free nilpotent group is a proper power.
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Prismatic F‐crystals and Wach modules
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract We show that the category of analytic/completed prismatic F-crystals$F\text{-crystals}$ on the absolute prismatic site of a small (unramified at p$p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of (φ,Γ)-modules$(\varphi, \Gamma)\text{-modules}$.
Abhinandan
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Nilpotency and Theory of L-Subgroups of an L-Group
Fuzzy Information and Engineering, 2014 In this paper, the notion of commutator is modified and extended to L-setting. Also, the notion of descending central series is introduced which is used to formulate the important notion of nilpotent L-subgroup of an L-group.
Naseem Ajmal, Iffat Jahan
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The singularity category and duality for complete intersection groups
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract If G$G$ is a finite group, the structure of the modular representation theory depends on the cochains C∗(BG;k)$C^*(BG; k)$, viewed as a commutative ring spectrum. We consider here its singularity category (in the sense of the author and Stevenson [Adv. Math.
J. P. C. Greenlees
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The structure of finite groups and ɵ-pairs of general subgroups
Open Mathematics, 2015 Using the concept of ɵ-pairs of proper subgroups of a finite group, we obtain some critical conditions of the supersolvability and nilpotency of finite groups.
Xu Yong, Hou Hailong, Zhang Xinjian
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On the cohomology of finite‐dimensional nilpotent groups and Lie rings
Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.Abstract We establish vanishing results for the first cohomology group of nilpotent groups and Lie rings when the submodule of invariants is trivial. Our results are obtained within a model‐theoretic setting, namely for structures that are definable in a finite‐dimensional theory, which encompasses algebraic groups over algebraically closed fields ...
Samuel Zamour
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Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
Complex Manifolds, 2017 Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t.
Yamada Takumi
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The N‐prime graph and the Subgroup Isomorphism Problem
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We introduce a directed graph related to a group G$G$, which we call the N‐prime graph ΓN(G)$\Gamma _{\rm {N}}(G)$ of G$G$ and is a refinement of the classical Gruenberg–Kegel graph. The vertices of ΓN(G)$\Gamma _{\rm {N}}(G)$ are the primes p$p$ such that G$G$ has an element of order p$p$, and, for distinct vertices p$p$ and q$q$, the arc q→p$
Emanuele Pacifici +2 more
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Actions of nilpotent groups on nilpotent groups
Glasgow Mathematical JournalAbstractFor finite nilpotent groups $J$ and $N$ , suppose $J$ acts on $N$ via automorphisms. We exhibit a decomposition of the first cohomology set in terms of the first cohomologies of the Sylow $p$ -subgroups of $J$ that mirrors the primary decomposition of $H^1(J,N)$ for abelian $N$ .
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Independence and strong independence complexes of finite groups
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract Let G$G$ be a finite group. In [10], two different concepts of independence (namely, independence and strong independence) are introduced for the subsets of G$G$, yielding to the definition of two simplicial complexes whose vertices are the elements of G$G$. The strong independence complex Σ∼(G)$\tilde{\Sigma }(G)$ turns out to be a subcomplex
Andrea Lucchini, Mima Stanojkovski
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