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- W2105847370 abstract "A class of groups F a,b,c having two generators and two relations is studied. This class is of interest for two reasons. It is relevant to the study of trivalent O-symmetric graphs and also adds infinite families to the known class of finite groups with two-generator two-relation presentations. Adding a third relation to the presentation for F a’b’c gives a homomorphic image H a’b’c . In this paper the orders of the groups H a’b’c are determined, also the orders of certain subclasses of the groups F a’b’c . Finally a conjecture is given concerning the normal subgroup G such that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:msup> <mml:mo>≅</mml:mo> <mml:msup> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> </mml:math> ." @default.
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- W2105847370 date "1977-11-21" @default.
- W2105847370 modified "2023-09-23" @default.
- W2105847370 title "Some families of finite groups having two generators and two relations" @default.
- W2105847370 cites W2052414950 @default.
- W2105847370 doi "https://doi.org/10.1098/rspa.1977.0177" @default.
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