By Kar Ping Shum, Zhe-Xian Wan, Jiping Zhang

On Normalized desk Algebras Generated by means of a devoted Non-Real section of measure three (Z Arad & G Chen); Graph Semigroups (V Dlab & T Pospichal); Moor-Penrose Generalized Inverses of Matrices Over department jewelry (Z-X Wan); M-Solid Pseudovarieties and Galois Connections (K Denecke & B Pibaljommee); Indecomposable Decompositions of CS-Modules (J L Gomez Pardo & P A Guil Asensio); Hereditary jewelry, QF2 earrings and earrings of Finite illustration sort (C R Hajarnavis); sturdy Burst errors Detecting Cyclic Codes (S Jain); at the Homology Bifunctors Over Semimodules (X T Nguyen); a few difficulties and Conjectures in Modular Representations (J-P Zhang); and different papers

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Robinson. Criteria for permutability to be transitive in finite groups. J . Algebra, 222(2):400-412, 1999. 9. J. C. Beidleman and H. Heineken. Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups. Preprint. 10. D. J. S. Robinson. Minimality and Sylow-permutability in locally finite groups. Preprint. 11. D. J. S. Robinson. The structure of finite groups in which permutability is a transitive relation. J . Austral. Math. Ser. A, 70:143-159, 2001. 12. G. Zacher.

Math. ,64(3):479-486, 2001. 45 14. M. J. Alejandre, A. Ballester-Bolinches, and M. C. Pedraza-Aguilera. Finite soluble groups with permutable subnormal subgroups. J. Algebra, 240(2):705721, 2001. 15. T. A. Peng. Finite groups with pronormal subgroups. Proc. Amer. Math. , 20:232-234, 1969. 16. M. Bianchi, A. Gillio Berta Mauri, M. Herzog, and L. Verardi. On finite solvable groups in which normality is a transitive relations. J. Group Theory, 3(2):147-156, 2000. 17. K. H. Miiller. Schwachnormale Untergruppen: Eine gemeinsame Verallgemeinerung der normalen und normalisatorgleichen Untergruppen.

Also the quotient table algebra with basis B32/C is strictly isomorphic the table algebra induced by the cyclic group Z6 of order 6. 5. lo), B22) One can derived from this table that B 2 2 = U:=,BbZ; = U ~ o , o S band $ b3 is a faithful element of B22 generates B 2 2 . Also the quotient table algebra with basis B22/C is strictly isomorphic to the table algebra induced by the cyclic group Z4 of order 4. The proofs related to our results are too long for the proceeding of the conference and we plan to send them for publication elsewhere.

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