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Note on a paper of Tsuzuku
- Source :
- Proceedings of the Glasgow Mathematical Association. 6:196-197
- Publication Year :
- 1964
- Publisher :
- Cambridge University Press (CUP), 1964.
-
Abstract
- In [2], Tosiro Tsuzzuku gave a proof of the following:THEOREM. Let G be a doubly transitive permutation group of degree n, let K be any commutative ring with unit element and let p be the natural representation of G by n × n permutation matrices with elements 0, 1 in K. Then ρ is decomposable as a matrix representation over K if and only ifn is an invertible element of K.For G the symmetric group this result follows from Theorems (2.1) and (4.12) of [1]. The proof given by Tsuzuku is unsatisfactory, although it is perfectly valid when K is a field. The purpose of this note is to give a correct proof of the general case.
Details
- ISSN :
- 20512104 and 20406185
- Volume :
- 6
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Glasgow Mathematical Association
- Accession number :
- edsair.doi...........3103b8677273333a84cfc8aef11362ca