説明
<p>The study of one-relator groups includes the connections between group properties and the form of the relator. In this paper we discuss conditions on the form <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Superscript negative 1 Baseline v Superscript l Baseline u v Superscript m"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>u</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>v</mml:mi> <mml:mi>l</mml:mi> </mml:msup> </mml:mrow> <mml:mi>u</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>v</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">{u^{ - 1}}{v^l}u{v^m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which force the corresponding one-relator groups to be nonresidually finite, i.e. the intersection of the normal subgroups of finite index to be nontrivial. Moreover we show that these forms can be detected amongst the words of a free group.</p>
収録刊行物
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- Transactions of the American Mathematical Society
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Transactions of the American Mathematical Society 164 (0), 105-114, 1972
American Mathematical Society (AMS)
