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dc.contributor.advisorCampbell, C. M. (Colin Matthew)
dc.contributor.authorGill, David Michael
dc.coverage.spatial81 p.en_US
dc.description.abstractWe consider two classes of groups with two generators and three relations. One class has a similar presentation to groups considered in the paper by C.M. Campbell and R.M. Thomas, ‘On (2,n)-Groups related to Fibonacci Groups’, (Israel J. Math., 58), with one generator of order three instead of order two . We attempt to find the order of these groups and in one case find groups which have the alternating group A₅ as a subgroup of index equal to the order of the second generator of the group. Questions remain as to the order of some of the other groups. The second class has already been considered in the paper 'Some families of finite groups having two generators and two relations' by C.M. Campbell , H.S.M. Coxeter and E.F. Robertson, (Proc. R. Soc. London A. 357, 423-438 (1977)), in which a formula for the orders of these groups was found. We attempt to find simpler formulae based on recurrence relations for subclasses and write Maple programs to enable us to do this. We also find a formula, again based on recurrence relations, for an upper bound for the orders of the groups.en_US
dc.publisherUniversity of St Andrews
dc.subject.lcshPresentations of groups (Mathematics)en
dc.titleSome group presentations with few defining relationsen_US
dc.type.qualificationnameMSc Master of Scienceen_US
dc.publisher.institutionThe University of St Andrewsen_US

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