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• W1994682593 abstract "We characterize the structure of the normal subgroup lattice of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2><mml:semantics><mml:mn>2</mml:mn><mml:annotation encoding=application/x-tex>2</mml:annotation></mml:semantics></mml:math></inline-formula>-transitive automorphism groups<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis normal upper Omega right-parenthesis><mml:semantics><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>A(Omega )</mml:annotation></mml:semantics></mml:math></inline-formula>of infinite chains<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis normal upper Omega comma less-than-or-slanted-equals right-parenthesis><mml:semantics><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo>,</mml:mo><mml:mo>⩽<!-- ⩽ --></mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>(Omega , leqslant )</mml:annotation></mml:semantics></mml:math></inline-formula>by the structure of the Dedekind completion<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis normal upper Omega overbar comma less-than-or-slanted-equals right-parenthesis><mml:semantics><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mover><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>¯<!-- ¯ --></mml:mo></mml:mover></mml:mrow><mml:mo>,</mml:mo><mml:mo>⩽<!-- ⩽ --></mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>(bar Omega , leqslant )</mml:annotation></mml:semantics></mml:math></inline-formula>of the chain<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis normal upper Omega comma less-than-or-slanted-equals right-parenthesis><mml:semantics><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo>,</mml:mo><mml:mo>⩽<!-- ⩽ --></mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>(Omega , leqslant )</mml:annotation></mml:semantics></mml:math></inline-formula>. As a consequence we obtain various group-theoretical results on the normal subgroups of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis normal upper Omega right-parenthesis><mml:semantics><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>A(Omega )</mml:annotation></mml:semantics></mml:math></inline-formula>, including that any proper subnormal subgroup of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis normal upper Omega right-parenthesis><mml:semantics><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>A(Omega )</mml:annotation></mml:semantics></mml:math></inline-formula>is indeed normal and contained in a maximal proper normal subgroup of<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis normal upper Omega right-parenthesis><mml:semantics><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>A(Omega )</mml:annotation></mml:semantics></mml:math></inline-formula>, and that<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis normal upper Omega right-parenthesis><mml:semantics><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>A(Omega )</mml:annotation></mml:semantics></mml:math></inline-formula>has precisely<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=5><mml:semantics><mml:mn>5</mml:mn><mml:annotation encoding=application/x-tex>5</mml:annotation></mml:semantics></mml:math></inline-formula>normal subgroups if and only if the coterminality of the chain<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis normal upper Omega comma less-than-or-slanted-equals right-parenthesis><mml:semantics><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo>,</mml:mo><mml:mo>⩽<!-- ⩽ --></mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>(Omega , leqslant )</mml:annotation></mml:semantics></mml:math></inline-formula>is countable." @default.
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• W1994682593 title "Normal subgroups of doubly transitive automorphism groups of chains" @default.
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