Periodic groups saturated with L 3(2m)

Lytkina, D. V.; Mazurov, V. D.

doi:10.1007/s10469-007-0033-z

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…This conjecture was confirmed in the case that every element of a saturating group set R is a finite simple group the centralizer of whose Sylow 2-subgroup contains no elements of odd order greater than 3 [1], and also in the cases R = {U 3 (9)} [2], R = {L 3 (11)} [3], and R = {L 3 (27)} [4].…”

Section: Introductionmentioning

confidence: 74%

The periodic groups saturated by finitely many finite simple groups

Lytkina¹,

Tukhvatullina²,

Filippov³

2008

Sib Math J

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Denote by M the set whose elements are the simple 3-dimensional unitary groups U 3 (q) and the linear groups L 3 (q) over finite fields. We prove that every periodic group, saturated by the groups of a finite subset of M, is finite.Keywords: saturation of a group by a set of groups, periodic group Introduction. A group G is called saturated by groups in some set R if each finite subgroup of G is contained in a subgroup of G isomorphic to some group in R. Take some group G saturated by groups in R and suppose that to X ∈ R there is a subgroup L of G isomorphic to X. In this case we say that G is saturated by R and call R a saturating group set for G.It was conjectured [1] that each periodic group is finite that is saturated by finitely many nonabelian simple groups. This conjecture was confirmed in the case that every element of a saturating group set R is a finite simple group the centralizer of whose Sylow 2-subgroup contains no elements of odd order greater than 3 [1], and also in the casesDenote by δ the variable taking the values + and −. Denote by L δ 3 (p n ) the group L 3 (p n ) if δ = + and the group U 3 (p n ) if δ = −.

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Section: Introductionmentioning

confidence: 74%

The periodic groups saturated by finitely many finite simple groups

Lytkina¹,

Tukhvatullina²,

Filippov³

2008

Sib Math J

Self Cite

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show abstract

“…In [1,[3][4][5], this conjecture was confirmed for the cases where M consists of, respectively, Ree groups, projective special linear groups of dimension 2, Suzuki groups, and projective special linear groups of dimension 3 over fields of even order.…”

Section: Introductionmentioning

confidence: 94%

Periodic groups saturated by finite simple groups U 3(2m)

Lytkina¹,

Tukhvatullina

Filippov

2008

Algebra Logic

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“…The lemma is proved. Now the argument in [11,Sec. 6] can be applied word for word to prove that in the case where G contains a dihedral group of order 8, G is isomorphic to L 3 (Q) for some locally finite field Q of characteristic 2.…”

Section: Lemma 213mentioning

confidence: 99%

“…Proofs of Lemmas 2.16-2.22 are identical to corresponding proofs of Lemmas 4.1-4.7 in [11] and so omitted. LEMMA 2.16.…”

Section: Lemma 213mentioning

confidence: 99%