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- W1977516048 abstract "A subgroup of the linear translation complement of a translation plane is geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for geometrically primitive. If a group is geometrically primitive and solvable then it is fixed point free or metacyclic or has a normal subgroup of order<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$w^{2a + b} $><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:msup></mml:math>where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$w^a $><mml:msup><mml:mi>w</mml:mi><mml:mi>a</mml:mi></mml:msup></mml:math>divides the dimension of the vector space. Similar conditions hold for solvable normal subgroups of geometrically primitive nonsolvable groups. When the dimension of the vector space is small there are restrictions on the group which might possibly be in the translation complement. We look at the situation for certain orders of the plane." @default.
- W1977516048 created "2016-06-24" @default.
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- W1977516048 date "1981-01-01" @default.
- W1977516048 modified "2023-09-25" @default.
- W1977516048 title "Collineation groups of translation planes of small dimension" @default.
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- W1977516048 doi "https://doi.org/10.1155/s0161171281000549" @default.
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