Über einfache endliche gruppen mit sylow-2-gruppen der ordnung höchstens 2<sup>10</sup>

Beisiegel, Bert

doi:10.1080/00927877708822162

Cited by 29 publications

(7 citation statements)

References 20 publications

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“…But then Theorem A and the classification of all finite simple groups whose Sylow 2-subgroups have order dividing 2 10 (cf. [4] and [7]) yield Theorem B. Consequently Theorem B is a consequence of Theorem A.…”

Section: A Let G Be a Finite Group With F*(g) Simple Assume That G mentioning

confidence: 74%

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

Harris¹

1980

Pacific J. Math.

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Section: A Let G Be a Finite Group With F*(g) Simple Assume That G mentioning

confidence: 74%

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

Harris¹

1980

Pacific J. Math.

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“…In view of Lemma 1.16 (f) and Lemma 2.8 for the remaining cases for o(a) it is enough to consider subgroups U of G such that either 31.6711 U] or 37"6711U 1. A direct inspection of the groups listed in [4] shows that U cannot be a proper subgroup of G. So the lemma is shown. …”

Section: N(e)/e~-a 5 Then Txc~((t)× L3(4))= {T} For Clearly Nx(e ) mentioning

confidence: 96%

“…7" 11"23 and Frob (11 "2) (vi) 215"35"53'7 • 11 "23 and Frob (11.5) (vii) 2 is "36 '53 "7" 11 "23 and Frob (11" 10) As p-local subgroups (p :p 23) are not divisible by 23, we thus see by Frattini's argument, that X is a simple group. Hence, a direct inspection of the groups with S2-subgroups of order not greater than 2 l° (see [4]) yields that the orders in (i), (ii), and (iii) are not possible. Assume case (iv) or (v).…”

Section: Hence the Group Cg(t)/(t)=(m~m2) Fixes Z Thus The Set Of mentioning

confidence: 99%

“…By inspection, see [18] we may assume that S2-subgroups of X have sectional 2-rank greater than 4. Obviously X contains an involution t such that 7 [[ C x (t)[ and so since t corresponds with a non-2-central involution in G we get that either S2-subgroups of Cx(t) are 4-groups or dihedral groups of order 8, in which cases the sectional 2-rank of X is at most 4, or Cx(t)(~) ~-L3(2) or L3 (4). Assume Cx(t) (~°)~-L3(2) and so since S2-subgroups have sectional 2-rank greater than 4, we obtain Cx(t)~ E 4 x La (2 ) or (E 4 x L3(2)).2.…”

Section: Hence the Group Cg(t)/(t)=(m~m2) Fixes Z Thus The Set Of mentioning

confidence: 99%

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On finite simple groups containing perspectivities

Reifart

Stroth

1982

Geom Dedicata

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PERSPECTIVITIESOne of the most fundamental results in the theory of projective planes is due to R. Baer: Let ~ be a projective plane and i a collineation of ~ of order 2, then either i is a perspectivity or planar.There are almost no general results dealing with collineation groups all of whose involutions are planar. Conversely, if a collineation group contains perspectivities of order 2, then a bunch of general theorems are available. Even if the restriction on the order of a perspectivity is dropped, still better results are known. A milestone among these is the following fundamental theorem due to Chr. Hering [25] : Let G be a finite collineation group acting strongly irreducibly on a projective plane ~. If G contains perspectivities, then with one exception G is an automorphism group of a non-abelian simple group.Geometriae Dedicata 13 (1982) 07-46. 0046-5755/82/0131-007506.00. Proof. The list of maximal subgroups can be found in [44] ; for the remaining statements see [31]. LEMMA 1.3. Let G be isomorphic with Mathieu's group M22. Then the following holds."(a) [GI = 27"32"5"7"11. (b) If M is a maximal subgroup of G, then M ~ La(4), E16 '2~5' E16"A6, AT, E 8 • L3(2), L2(11 ), or A6"2. (c) All involutions in G are conjugate and if t is an involution in G, then C~(t) = E16"24, a subgroup of the maximal subgroup E16'A6.Proof. The list of maximal subgroups can be found in [6], whereas for the remaining statements see [35].

show abstract

“…From [4] we can write down a fragment of the character table of fl (Table 2). According to [7], we may assume in cases a)-c) that A is a known simple group.…”

Section: Preliminary Lemmasmentioning

confidence: 99%

Wide subgroups of some sporadic groups

Chekanov¹

1990

Algebra and Logic

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Über einfache endliche gruppen mit sylow-2-gruppen der ordnung höchstens 2¹⁰

Cited by 29 publications

References 20 publications

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

On finite simple groups containing perspectivities

Wide subgroups of some sporadic groups

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Über einfache endliche gruppen mit sylow-2-gruppen der ordnung höchstens 210

Cited by 29 publications

References 20 publications

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

Finite groups having an involution centralizer with a 2-component of type PSL(3,3)

On finite simple groups containing perspectivities

Wide subgroups of some sporadic groups

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Über einfache endliche gruppen mit sylow-2-gruppen der ordnung höchstens 2¹⁰