Let n be a non-zero positive integer and (n) the set of all partitions of n. There is a oneto-one correspondence between (n) and the set of the conjugacy classes of S n , the symmetric group of degree n. Let X (S n ) = (S n , {R \* Ξ» } Ξ»β (n) ) be the group association scheme of S n and X = (X, {R Ξ»
Characterization of the Group Association Scheme of PSL(2, 7)
β Scribed by Masato Tomiyama
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 328 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0097-3165
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β¦ Synopsis
The association scheme having the same intersection numbers as those of the group association scheme X(PSL(2, 7)) is shown to be isomorphic to X(PSL(2, 7)), where PSL(2, 7) is the 2-dimensional projective special linear group over the field of order 7.
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It is shown that the group association scheme for the split extension of 2 3 by SL 3 (2) is not isomorphic to that for the non-split extension , although they have the same set of parameters (intersection numbers) .