Results 61 to 70 of about 46,068 (245)
The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
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On the solvability of the Lie algebra HH1(B)$\mathrm{HH}^1(B)$ for blocks of finite groups
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We give some criteria for the Lie algebra HH1(B)$\mathrm{HH}^1(B)$ to be solvable, where B$B$ is a p$p$‐block of a finite group algebra, in terms of the action of an inertial quotient of B$B$ on a defect group of B$B$.
Markus Linckelmann, Jialin Wang
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On the Mislin genus of certain circle bundles and noncancellation
International Journal of Mathematics and Mathematical Sciences, 2000 In an earlier paper, the authors proved that a process described much earlier for passing from a finitely generated nilpotent group N of a certain kind to a nilpotent space X of finite type produced a bijection of Mislin genera 𝒢(N)≅𝒢(X).
Peter Hilton, Dirk Scevenels
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GL‐algebras in positive characteristic II: The polynomial ring
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
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Some results on characterization of finite group by non commuting graph [PDF]
Transactions on Combinatorics, 2012 The non commuting graph of a non-abelian finite group $G$ is defined as follows: its vertex set is $G-Z(G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity.
Mohammad Reza Darafsheh +1 more
doaj
Countingp-groups and nilpotent groups [PDF]
Publications mathématiques de l'IHÉS, 2000 What can one say about the function \(f(p,n)\) that counts (up to isomorphism) groups of order \(p^n\), where \(p\) is a prime, and \(n\) is an integer? \textit{G. Higman} [Proc. Lond. Math. Soc. (3) 10, 24-30 (1960; Zbl 0093.02603)] and \textit{C. C. Sims} [Proc. Lond. Math. Soc. (3) 15, 151-166 (1965; Zbl 0133.28401)] have given an asymptotic formula
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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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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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On Malle’s conjecture for nilpotent groups
Transactions of the American Mathematical Society, Series B, 2023 We develop an abstract framework for studying the strong form of Malle’s conjecture [J. Number Theory 92 (2002), pp. 315–329; Experiment. Math. 13 (2004), pp. 129–135] for nilpotent groups G G in their regular representation. This framework is then used to prove the strong form of Malle’s conjecture for any nilpotent group G
Koymans, P., Pagano, C.
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