Solution of the Burnside problem for exponent six

Hall, Marshall

doi:10.1215/ijm/1255448339

Cited by 47 publications

(29 citation statements)

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“…The theorem gives an affirmative answer to question 16.56 in [2]. Together with results in [3][4][5][6][7][8][9][10][11][12], the theorem implies the following:…”

mentioning

confidence: 57%

“…where j 1 , j 2 ∈ {4, 6}, which either equals K (6,4) S 5 or has order 2. Both of these cases are impossible.…”

Section: The Notation and Preliminary Resultsmentioning

confidence: 99%

“…These relations define a representation for A 6 . Put (2) There exists an involution t ∈ Γ 2 (G)\H for which…”

Section: Lemma 14mentioning

confidence: 99%

“…x = ac = (1, 5)(2, 3), y = cd = (1, 6)(2, 5), and z = ab = (1, 5)(2, 3).Suppose V = x, x a and s = x abcad = (2, 5)(4,6);then N H (V ) = V c, s V S 3 S 4 . Let V 1 be as in Lemma 14.…”

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confidence: 99%

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Groups Whose Element Orders do not Exceed 6

et al. 2014

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It is proved that a periodic group whose element orders do not exceed 6 either is a locally finite or is group of exponent 5.The spectrum of a group G is the set ω(G) of its element orders. The objective of the present paper is to prove THEOREM. If the spectrum of a group G is equal to {1, 2, 3, 4, 5, 6}, then G is locally finite and satisfies one of the following:(where C is isomorphic to SL 2 (3) or to a group x, y | x 3 = y 4 = 1, x y = x −1 , and C acts freely on N ;(2) T = O 2 (G) is a nontrivial elementary Abelian group and G/T is isomorphic to A 5 ;(3) G is isomorphic to S 5 or S 6 . Hereinafter, O p (G), where p is a prime, denotes the greatest normal p-subgroup of G; A n and S n stand for, respectively, the alternating group of degree n and the symmetric group of degree n. A group A freely acts on a group B if A acts on B, B is nontrivial, and b a = b if a and b are nontrivial elements of A and B, respectively.

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“…The theorem gives an affirmative answer to question 16.56 in [2]. Together with results in [3][4][5][6][7][8][9][10][11][12], the theorem implies the following:…”

mentioning

confidence: 57%

“…where j 1 , j 2 ∈ {4, 6}, which either equals K (6,4) S 5 or has order 2. Both of these cases are impossible.…”

Section: The Notation and Preliminary Resultsmentioning

confidence: 99%

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Groups Whose Element Orders do not Exceed 6

et al. 2014

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“…The groups with ω(G) = {1, 2, 3} are described in [3]. The local finiteness of a group whose element orders do not exceed 4 is proved in [4]; and of a group of period 6, in [5]. The structure of G with ω(G) = {1, 2, 5} is described in [6].…”

Section: Introductionmentioning

confidence: 99%