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Displaying 41 – 60 of 147

Finite simple groups of Lie type as expanders

Alexander Lubotzky (2011)

Journal of the European Mathematical Society

We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for ${S L}_{2}$ which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.

Generators for finite groups with a unique minimal normal subgroup

Andrea Lucchini, Federico Menegazzo (1997)

Rendiconti del Seminario Matematico della Università di Padova

Generators of an orthogonal group over a finite field

Hiroyuki Ishibashi (1978)

Czechoslovak Mathematical Journal

Generic $2$ -coverings of finite groups of Lie type

D. Bubboloni, M. S. Lucido, Th. Weigel (2006)

Rendiconti del Seminario Matematico della Università di Padova

Groups generated by two mutually Engel periodic elements

H. Heineken (2000)

Bollettino dell'Unione Matematica Italiana

Scriviamo $[x, y] = [x,_{1} y]$ ed $[[x,_{k} y], y] = [x,_{k + 1} y]$ . Cerchiamo gruppi $S L (2, q)$ con generatori $x, y$ tali che $[x,_{m} y] = x$ ed $[y,_{n} x] = y$ per alcuni numeri naturali $m$ , $n$ .

Groups saturated by a finite set of groups.

Shlepkin, A.K., Rubashkin, A.G. (2004)

Sibirskij Matematicheskij Zhurnal

Groups with a Steinberg Character.

Forrest A. Richen (1972)

Mathematische Zeitschrift

Groups with root-system of type $B C_{ℓ}$ .

Timmesfeld, Franz Georg (2003)

Beiträge zur Algebra und Geometrie

Intersecting families in the alternating group and direct product of symmetric groups.

Ku, Cheng Yeaw, Wong, Tony W.H. (2007)

The Electronic Journal of Combinatorics [electronic only]

Intersection graphs of subgroups of finite groups

Rulin Shen (2010)

Czechoslovak Mathematical Journal

In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.

Nested symmetric representation of elements of the Suzuki chain groups.

Sayed, Mohamed (2003)

International Journal of Mathematics and Mathematical Sciences

New characterization of $S_{4} (q)$ by its noncommuting graph.

Zhang, Liangcai, Shi, Wujie (2009)

Sibirskij Matematicheskij Zhurnal

Nonassociativity in VOA theory and finite group theory

Jr. Griess, Robert L. (2010)

Commentationes Mathematicae Universitatis Carolinae

We discuss some examples of nonassociative algebras which occur in VOA (vertex operator algebra) theory and finite group theory. Methods of VOA theory and finite group theory provide a lot of nonassociative algebras to study. Ideas from nonassociative algebra theory could be useful to group theorists and VOA theorists.

Non-existence de certains polygones généralisés. II.

J. Tits (1979)

Inventiones mathematicae

OD-characterization of almost simple groups related to $L_{2} (49)$

Liang Cai Zhang, Wu Jie Shi (2008)

Archivum Mathematicum

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_{2} (49)$ . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_{2} (49)$ except $L_{2} (49) \cdot 2^{2}$ . Also, we prove that if $M$ is an almost simple group related to $L_{2} (49)$ except $L_{2} (49) \cdot 2^{2}$ and $G$ is a finite group such that $| G | = | M |$ and $Γ (G) = Γ (M)$ , then $G ≅ M$ .

Currently displaying 41 – 60 of 147

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