The Burnside problem

Kostrikin, Α. I.

doi:10.1090/trans2/036/03

Cited by 17 publications

(17 citation statements)

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“…The classification of finite simple groups [9] implies that the assumptions made by Hall and Higman are valid. The restricted Burnside problem for prime exponent was solved by Kostrikin in 1959 (see [21,22]), but it was a further 30 years before Zel'manov [45,46] solved it for all prime-power exponents p …”

Section: Are There Only Finitely Many Finite M-generator Groups Of Exmentioning

confidence: 99%

Bounds in the restricted Burnside problem

Vaughan-Lee¹,

Zelmanov²

1999

J Aust Math Soc A

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Section: Are There Only Finitely Many Finite M-generator Groups Of Exmentioning

confidence: 99%

Bounds in the restricted Burnside problem

Vaughan-Lee¹,

Zelmanov²

1999

J Aust Math Soc A

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“…Following A. I. Kostrikin [Kos1,Kos3], we call an element a of a Lie algebra L a sandwich if (i) ad(a) 2 = 0 and (ii) ad(a) ad(b) ad(a) = 0 for an arbitrary element b ∈ L.…”

Section: This Theorem Has Implications In Group Theorymentioning

confidence: 99%

Lie algebras and torsion groups with identity

Zelmanov¹

2017

J. Comb. Algebra

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“…By results of Adjan and Novikov [1], there exists, for each sufficiently large odd integer p, a finitely generated infinite group H of exponent p. Now if p is prime, then by a theorem of Kostrikin [10] there is a finite bound on the indices of the subgroups of finite index in H. Hence H has only finitely many subgroups of finite index, and their intersection JV also has finite index in H. Thus JV is finitely generated, so JV has a maximal proper normal subgroup M. By definition of JV, | JV : M\ is infinite, so N/M is an infinite simple group of exponent p.…”

Section: Infinite Simple Groupsmentioning

confidence: 99%

Varieties and simple groups

Jones

1974

J. Aust. Math. Soc.

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In her book on varieties of groups, Hanna Neumann posed the following problem [13, p. 166]: “Can a variety other than D contain an infinite number of non-isomorphic non-abelian finite simple groups?”The answer to this question does not seem to be known at present. However, in [7], Heineken and Neumann described an algorithm for determining whether or not there are any non-abelian finite simple groups satisfying a given law. They also outlined a way in which their algorithm could be used to show that “only finitely many of the known non-abelian finite simple groups can satisfy a given non-trivial law”; in this paper, we shall follow their suggestions, and prove theTHEOREM. Let g be a set of mutually non-isomorphic non-abelian finite simple groups, each of which is either an alternating group or a group of Lie type, and let g generate a proper subvariety of D. Then y is finite.

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The Burnside problem

Cited by 17 publications

References 0 publications

Bounds in the restricted Burnside problem

Bounds in the restricted Burnside problem

Lie algebras and torsion groups with identity

Varieties and simple groups

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