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

Lytkina, D. V.; Tukhvatullina, L. R.; Filippov, K. A.

doi:10.1007/s10469-008-9011-3

Cited by 7 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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