Modular invariant theory: Difference between revisions

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{{Short description|Sub-field of mathematics}}

In [[mathematics]], a '''modular invariant''' of a [[group (mathematics)|group]] is an invariant of a [[finite group]] [[Group action (mathematics)|acting]] on a [[vector space]] of positive characteristic (usually dividing the [[order (group theory)|order]] of the group). The study of modular invariants was originated in about 1914 by {{harvtxt|Dickson|2004}}.

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==References==

*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=A Fundamental System of Invariants of the General Modular Linear Group with a Solution of the Form Problem | jstor=1988736 | year=1911 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=12 | issue=1 | pages=75–98 | doi=10.2307/1988736| doi-access=free }}

*{{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=On invariants and the theory of numbers | origyearorig-date=1914 | url=https://books.google.com/books?isbn=0486438287 | publisher=[[Dover Publications]] | ___location=New York | series=Dover Phoenix editions | isbn=978-0-486-43828-3 | mr=0201389 | year=2004}}

*{{Citation | last1=Rutherford | first1=Daniel Edwin | authorlink=Daniel Edwin Rutherford | title=Modular invariants | origyearorig-date=1932 | url=https://archive.org/details/modularinvariant033204mbp | publisher=Ramsay Press | series=Cambridge Tracts in Mathematics and Mathematical Physics, No. 27 | isbn=978-1-4067-3850-6 | mr=0186665 | year=2007}}

*{{Citation | last1=Sanderson | first1=Mildred | authorlink=Mildred Sanderson | title=Formal Modular Invariants with Application to Binary Modular Covariants | jstor=1988702 | year=1913 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=14 | issue=4 | pages=489–500 | doi=10.2307/1988702| doi-access=free }}

*{{Citation | last1=Steinberg | first1=Robert | authorlink=Robert Steinberg | title=On Dickson's theorem on invariants | url=http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/1682/1/jfs340309.pdf | mr=927606 | year=1987 | journal=Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics | issn=0040-8980 | volume=34 | issue=3 | pages=699–707 | access-date=2010-12-02 | archive-url=https://web.archive.org/web/20120305205421/http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/1682/1/jfs340309.pdf | archive-date=2012-03-05 | url-status=dead }}