Results 51 to 60 of about 49,568 (240)
On stabilizers in finite permutation groups
Bulletin of the London Mathematical Society, EarlyView.Abstract Let G$G$ be a permutation group on the finite set Ω$\Omega$. We prove various results about partitions of Ω$\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set‐stabilizer whose orbits have length at most 6, which is best possible and answers two questions of Babai.
Luca Sabatini
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Regularity of extended conjugate graphs of finite groups
AIMS Mathematics, 2022 The extended conjugate graph associated to a finite group $ G $ is defined as an undirected graph with vertex set $ G $ such that two distinct vertices joined by an edge if they are conjugate.
Piyapat Dangpat, Teerapong Suksumran
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Journal of Functional Analysis, 1986 G denotes a simply-connected real nilpotent Lie group, L the Lie algebra of G, \(L_ 1=L\), \(L_{k+1}=[L_ k,L]\), \(d=\sum k \dim (L_ k/L_{k+1})=\) the Dirichlet dimension of G, \(\delta =\sum (m+1) \dim (K_{m+1}/K_ m)\), where \(K_ m\) (m\(\geq 0)\) denotes the subspace of L generated by all commutators of length \(\leq m\). Take \(X_ 1,...,X_ k\in L\)
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On nilpotent and polycyclic groups [PDF]
Bulletin of the Australian Mathematical Society, 1989 A group G is torsion-free, finitely generated, and nilpotent if and only if G is a supersolvable R-group. An ordered polycylic group G is nilpotent if and only if there exists an order on G with respect to which the number of convex subgroups is one more than the length of G.
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Residually rationally solvable one‐relator groups
Bulletin of the London Mathematical Society, EarlyView.Abstract We show that the intersection of the rational derived series of a one‐relator group is rationally perfect and is normally generated by a single element. As a corollary, we characterise precisely when a one‐relator group is residually rationally solvable.
Marco Linton
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On finitely generated left nilpotent braces
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract A description of finitely generated left nilpotent braces of class at most two is presented in this paper. The description heavily depends on the fact that if B$B$ is left nilpotent of class at most 2, that is B3=0$B^3 = 0$, then B$B$ is right nilpotent of class at most 3, that is B(4)=0$B^{(4)} = 0$. In addition, we construct a free object in
Hangyang Meng +3 more
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Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results
, 2018 In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold with a distinguished filtration of subbundles of the tangent bundle which is ...
Choi, Woocheol, Ponge, Raphael
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Real models for the framed little n$n$‐disks operads
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
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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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Journal of Algebra, 2006 AbstractIn this paper we prove some results concerning how much information about the structure of a finite group can be gained from knowledge of the set of sizes of the conjugacy classes. We give examples to show that in general nilpotency cannot be recognised.
Alan R. Camina, Rachel Camina
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