Groups St Andrews 1997 in Bath
Volume 2
Aner Shalev
Publisher: Cambridge University Press
Print Publication Year: 1999
Online Publication Date:August 2010
Online ISBN:9780511666148
Paperback ISBN:9780521655767
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511666148.028
Subjects: Algebra
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Abstract
In recent years there have been several developments in the study of probabilistic aspects of certain finite and profinite groups, and various conjectures in this field were settled. Moreover, the probabilistic approach led to the solution of interesting problems whose formulation had nothing to do with probability; these include problems regarding the modular group, free groups, as well as conjectures on finite permutation groups. In this lecture series I will try to survey these developments and discuss directions for further research.
Contents:
Finite simple groups: random generation
Group theory and measure theory seem to intersect highly non-trivially, and so there are many branches in mathematics which could be referred to as probabilistic group theory. In this lecture series I would like to focus on a relatively young area, which concerns probabilistic aspects of finite groups and their inverse limits. I shall also demonstrate how probabilistic ideas can be used to solve classical problems in finite and infinite groups.
A classical scheme, applied successfully in combinatorics, number theory, and other areas, is to prove existence theorems using a probabilistic approach. The idea is to show that most objects have a certain property, and then to deduce that an object with that property exists.
pp. i-iv
pp. v-viii
pp. ix-x
Galois groups through invariant relations: Read PDF
pp. 379-393
Construction of Co3. An example of the use of an integrated system for computational group theory: Read PDF
pp. 394-409
Embedding some recursively presented groups: Read PDF
pp. 410-416
The Dedekind-Frobenius group determinant: new life in an old problem: Read PDF
pp. 417-428
Group characters and π-sharpness: Read PDF
pp. 429-435
Permutation group algorithms via black box recognition algorithms: Read PDF
pp. 436-446
Nonabelian tensor products of groups: the commutator connection: Read PDF
pp. 447-454
Simple subalgebras of generalized Witt algebras of characteristic zero: Read PDF
pp. 455-459
Applications of the Baker-Hausdorff formula in the theory of finite p-groups: Read PDF
pp. 460-473
Generalizations of the restricted Burnside problem for groups with automorphisms: Read PDF
pp. 474-491
The ∑m -conjecture for a class of metabelian groups: Read PDF
pp. 492-502
Rings with periodic groups of units II: Read PDF
pp. 503-511
Some free-by-cyclic groups: Read PDF
pp. 512-516
The residually weakly primitive geometries of the Suzuki simple group Sz (8): Read PDF
pp. 517-526
Semigroup identities and Engel groups: Read PDF
pp. 527-531
Groups whose elements have given orders: Read PDF
pp. 532-537
The Burnside groups and small cancellation theory: Read PDF
pp. 538-559
Solvable Engel groups with nilpotent normal closures: Read PDF
pp. 560-567
Nilpotent injectors in finite groups: Read PDF
pp. 568-570
Some groups with right Engel elements: Read PDF
pp. 571-578
The growth of finite subgroups in p-groups: Read PDF
pp. 579-595
Symplectic amalgams and extremal subgroups: Read PDF
pp. 596-604
Primitive prime divisor elements in finite classical groups: Read PDF
pp. 605-623
On the classification of generalized Hamiltonian groups: Read PDF
pp. 624-632
Permutability properties of subgroups: Read PDF
pp. 633-638
When Schreier transversals grow wild: Read PDF
pp. 639-647
Probabilistic group theory: Read PDF
pp. 648-678
Combinatorial methods: from groups to polynomial algebras: Read PDF
pp. 679-688
Formal languages and the word problem for groups: Read PDF
pp. 689-700
Periodic cohomology and free and proper actions on ℝn × Sm : Read PDF
pp. 701-717
On modules over group rings of soluble groups of finite rank: Read PDF
pp. 718-727
On some series of normal subgroups of the Gupta-Sidki 3-group: Read PDF
pp. 728-737