Note on a paper of Tsuzuku
1964 ◽
Vol 6
(4)
◽
pp. 196-197
Keyword(s):
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.
1962 ◽
Vol 5
(3)
◽
pp. 121-136
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Keyword(s):
1933 ◽
Vol 29
(2)
◽
pp. 257-259
1984 ◽
Vol 36
(1)
◽
pp. 69-86
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1970 ◽
Vol 22
(2)
◽
pp. 193-201
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1936 ◽
Vol 5
(1)
◽
pp. 1-13
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Keyword(s):
1967 ◽
Vol 63
(3)
◽
pp. 647-652
◽
2002 ◽
Vol 65
(2)
◽
pp. 277-288
◽
1949 ◽
Vol 1
(2)
◽
pp. 125-152
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