Results 51 to 60 of about 993,639 (182)

A Higher Frobenius-Schur Indicator Formula for Group-Theoretical Fusion Categories

, 2015
Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: A finite group $G$ endowed with a three-cocycle $\omega$, and a subgroup $H\subset G$ endowed with a two-cochain whose coboundary is the restriction of
Schauenburg, Peter
core   +3 more sources

Finite groups whose coprime graph is split, threshold, chordal, or a cograph [PDF]

Proceedings of the Estonian Academy of Sciences
Given a finite group G, the coprime graph of G, denoted by Γ(G), is defined as an undirected graph with the vertex set G, and for distinct x, y ∈ G, x is adjacent to y if and only if (o(x), o(y)) = 1, where o(x) and o(y) are the orders of x and y ...
Jin Chen, Shixun Lin, Xuanlong Ma
doaj   +1 more source

Products of squares in finite simple groups [PDF]

Proceedings of the American Mathematical Society, 2011
The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange’s four squares theorem.
Liebeck, Martin W., O’Brien, E. A., Shalev, Aner, Tiep, Pham Huu   +3 more
openaire   +2 more sources

Quasirecognition by prime graph of U_3(q) where 2 < q =p^{alpha} < 100 [PDF]

International Journal of Group Theory, 2012
Let G be a finite group and let Gamma(G) be the prime graphof G. Assume 2 < q = p^{alpha} < 100 . We determine finite groupsG such that Gamma(G) = Gamma(U_3(q)) and prove that if q neq3, 5, 9, 17, then U_3(q) is quasirecognizable by prime graph,i.e., if ...
Ali Iranmanesh, Abolfazl Tehranian, Alireza Khalili Asboei, Seyed Sadegh Salehi Amiri   +3 more
doaj  

Probabilistic Generation of Finite Simple Groups

Journal of Algebra, 2000
It is well known that any finite group \(G\) can be generated by two elements and the probability that two elements generate \(G\) approaches 1 as the order of \(G\) goes to infinity. The paper under review deals with a more specific problem. As the main result the authors prove that for each finite almost simple group \(G\) there exists a conjugacy ...
Guralnick, Robert M., Kantor, William M.
openaire   +1 more source

Divisibility and laws in finite simple groups [PDF]

Mathematische Annalen, 2015
20 pages, no figures; v3 completely rewritten with new co-author and new ...
Gady Kozma, Andreas Thom
openaire   +3 more sources

$N$-recognizability of Groups $ Alt_p\times Alt_5$,\\ Where $p>1361$ Is a Prime Number

Известия Иркутского государственного университета: Серия "Математика"
$N$-recognizability of Groups $ Alt_p\times Alt_5$, Where $p>1361$ Is a Prime Number} Given a finite group $L$, let $N(L)$ denote the set of its conjugacy class sizes.
I. B. Gorshkov, V. D. Shepelev
doaj   +1 more source

A REFINED WARING PROBLEM FOR FINITE SIMPLE GROUPS

Forum of Mathematics, Sigma, 2015
Let $w_{1}$ and $w_{2}$ be nontrivial words in free groups $F_{n_{1}}$ and $F_{n_{2}}$, respectively. We prove that, for all sufficiently large finite nonabelian simple groups $G$, there exist subsets $C_{1}\subseteq w_{1}(G)$ and $C_{2}\subseteq w_{2}(G)
MICHAEL LARSEN, PHAM HUU TIEP
doaj   +1 more source

About Periodic Shunkov Group Saturated with Finite Simple Groups of Lie Type Rank 1

Известия Иркутского государственного университета: Серия "Математика", 2016
The property of group G to be saturated with given set of groups X is a natural generalization of locally-cover definition (in class of locally finite groups) on periodic groups. Locally-finite group, witch has a locally-cover contains from finite simple
A. Shlepkin
doaj  

Random Generation of Finite Simple Groups

Journal of Algebra, 1999
\textit{J. D. Dixon} [Math. Z. 110, 199-205 (1969; Zbl 0176.29901)] conjectured that if two elements are randomly chosen from a finite simple group \(G\), they will generate \(G\) with probability \(\to 1\) as \(|G|\to\infty\). Dixon [ibid.] proved this if \(G\) is an alternating group. \textit{W. M. Kantor} and \textit{A. Lubotzky} [Geom. Dedicata 36,
Guralnick, Robert M., Liebeck, Martin W., Saxl, Jan, Shalev, Aner   +3 more
openaire   +2 more sources