Simple groups, permutation groups, and probability.

Shalev, Aner

Displaying similar documents to “Simple groups, permutation groups, and probability.”

The Bass conjecture and growth in groups

Anders Karlsson, Markus Neuhauser (2004)

Colloquium Mathematicae

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We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.

On the exponent of the cokernel of the forget-control map on K₀-groups

Francis X. Connolly, Stratos Prassidis (2002)

Fundamenta Mathematicae

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For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.

On the maximal subgroups of the finite classical groups.

M. Aschbacher (1984)

Inventiones mathematicae

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Groups saturated by a finite set of groups.

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

Sibirskij Matematicheskij Zhurnal

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A condition for the solvability of finite groups.

Miao, Long, Qian, Guohua (2009)

Sibirskij Matematicheskij Zhurnal

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The Ore conjecture

Martin Liebeck, E.A. O’Brien, Aner Shalev, Pham Tiep (2010)

Journal of the European Mathematical Society

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The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

Groups satisfying the maximal condition on subnormal non-normal subgroups

Fausto De Mari, Francesco de Giovanni (2005)

Colloquium Mathematicae

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The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.