“Higman group”的意思、由来-开放百科全书

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Higman group

释义

References

In mathematics, the Higman group, introduced by {{harvs|txt|first=Graham|last=Higman|authorlink=Graham Higman|year=1951}}, was the first example of an infinite finitely presented group with no non-trivial finite quotients.

The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. {{harvtxt|Higman|1974}} later found some finitely presented infinite groups {{math|G{{sub|n,r}}}} that are simple if {{math|n}} is even and have a simple subgroup of index 2 if {{math|n}} is odd, one of which is one of the Thompson groups.

Higman's group is generated by 4 elements {{math|a, b, c, d}} with the relations

References

{{Citation | last1=Higman | first1=Graham | author1-link=Graham Higman | title=A finitely generated infinite simple group | doi=10.1112/jlms/s1-26.1.61 |mr=0038348 | year=1951 | journal=Journal of the London Mathematical Society |series=Second Series | issn=0024-6107 | volume=26 | issue=1 | pages=61–64}}
{{Citation | last1=Higman | first1=Graham | author1-link=Graham Higman | title=Finitely presented infinite simple groups | url=https://books.google.com/books?id=LPvuAAAAMAAJ | publisher=Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra | series=Notes on Pure Mathematics | isbn=978-0-7081-0300-5 |mr=0376874 | year=1974 | volume=8}}

1 : Group theory

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