Results 71 to 80 of about 67,282 (171)

Fixed‐point posets of groups and Euler characteristics

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract Suppose that G$G$ is a group and Ω$\Omega$ is a G$G$‐set. For X$\mathcal {X}$ a set of subgroups of G$G$, we introduce the fixed‐point poset XΩ$\mathcal {X}_{\Omega }$. A variety of results concerning XΩ$\mathcal {X}_{\Omega }$ are proved as, for example, in the case when p$p$ is a prime and X$\mathcal {X}$ is a non‐empty set of finite non ...
Peter Rowley
wiley   +1 more source

Upper ramification jumps in abelian extensions of exponent p

, 2014
In this paper we present a classification of the possible upper ramification jumps for an elementary abelian p-extension of a p-adic field. The fundamental step for the proof of the main result is the computation of the ramification filtration for the ...
Capuano, Laura, Del Corso, Ilaria
core  

Abelian $$p$$-groups with a fixed elementary subgroup or with a fixed elementary quotient

Archiv der Mathematik
Abstract In his 1934 paper, G. Birkhoff poses the problem of classifying pairs (G, U) where G is an abelian group and $$U\subset G$$ U ⊂ G a subgroup ...
Justyna Kosakowska, Markus Schmidmeier, Martin Schreiner   +2 more
openaire   +3 more sources

Groups with conjugacy classes of coprime sizes

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract Suppose that x$x$, y$y$ are elements of a finite group G$G$ lying in conjugacy classes of coprime sizes. We prove that ⟨xG⟩∩⟨yG⟩$\langle x^G \rangle \cap \langle y^G \rangle$ is an abelian normal subgroup of G$G$ and, as a consequence, that if x$x$ and y$y$ are π$\pi$‐regular elements for some set of primes π$\pi$, then xGyG$x^G y^G$ is a π ...
R. D. Camina, A. Maróti, E. Pacifici, C. Parker, K. Rekvényi, J. Saunders, V. Sotomayor, G. Tracey, M. van Beek   +8 more
wiley   +1 more source

Centralizers of elementary Abelian subgroups in finite p-groups

Journal of Algebra, 1978
In this paper we show that if P is a finite p-group with the elements of order p (orders 2 and 4, ifp = 2) central, then the commutator group P’ and the central factor group P/Z(P) h ave the same exponent. We obtain new proofs and analogs for p = 2 of two recent results of van der Waall [4, Theorems 2.31.
openaire   +2 more sources

Linear Diophantine equations and conjugator length in 2‐step nilpotent groups

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract We establish upper bounds on the lengths of minimal conjugators in 2‐step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp.
M. R. Bridson, T. R. Riley
wiley   +1 more source

A history of Galois fields

Khronos, 2016
This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
doaj  

Essential cohomology for elementary abelian p-groups

Journal of Pure and Applied Algebra, 2009
For an odd prime p the cohomology ring of an elementary abelian p-group is polynomial tensor exterior. We show that the ideal of essential classes is the Steenrod closure of the class generating the top exterior power. As a module over the polynomial algebra, the essential ideal is free on the set of Mui invariants.
Altunbulak Aksu, F., Green, D. J.
openaire   +6 more sources

Elementary abelian subgroups in p-groups with a cyclic derived subgroup

Journal of Algebra, 2011
Let \(P\) be a finite \(p\)-group with cyclic \(P'\), let \(\mathcal A_p(P)\) be the poset of all nontrivial elementary Abelian subgroups of \(P\) and let \(\mathcal A_p(P)_{\geq 2}=\{E\in\mathcal A_p(P)\mid |E|\geq p^2\}\). It was proved by \textit{S. Bouc} and \textit{J. Thévenaz}, [``The poset of elementary Abelian subgroups of rank at least \(2\)'',
openaire   +2 more sources

Solving Linear Constraints in Elementary Abelian p-Groups of Symmetries

, 2011
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of symmetries that can be huge, and the problem of their very existence is NP-hard.
de la Tour, Thierry Boy, Echenim, Mnacho
openaire   +2 more sources