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A complete classification of finite homogeneous groups

Published online by Cambridge University Press:  17 April 2009

Cai Heng Li
Affiliation:
Department of Mathematics, University of Western Australia, Perth. 6907 WA, Australia
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In this short note, we obtain a complete classification of finite homogeneous groups.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A., Atlas of finite groups (Clarendon Press, Oxford, 1985).Google Scholar
[2]Cherlin, G.L. and Felgner, U., ‘Quantifier eliminable groups’, in Logic Colloquium 1980, (van Dalen, , Editor) (North-Holland, Amsterdam, 1982), pp. 6981.Google Scholar
[3]Cherlin, G.L. and Felgner, U., ‘Homogeneous solvable groups’, J. London Math. Soc. (2) 44 (1991), 102120.Google Scholar
[4]Feit, W. and Seitz, G.M., ‘On finite rational groups and related topics’, Illinois J. Math. 33 (1989), 103131.CrossRefGoogle Scholar
[5]Li, C.H., ‘Isomorphisms of finite Cayley digraphs of bounded valency II’, J. Combin. Theory Ser. A (to appear).Google Scholar
[6]Li, C.H. and Praeger, C.E., ‘The finite simple groups with at most two fusion classes of every order’, Comm. Algebra 24 (1996), 36813704.Google Scholar
[7]Li, C.H. and Praeger, C.E., ‘Finite groups in which any two elements of the same order are either fused or inverse-fused’, Comm. Algebra 25 (1996), 30813118.Google Scholar
[8]Li, C.H., Praeger, C.E. and Xu, M.Y., ‘Isomorphisms of finite Cayley digraphs of bounded valency’, J. Combin. Theory Ser. B 73 (1998), 164183.Google Scholar
[9]Stroth, G., ‘Isomorphic subgroups’, Comm. Algebra 24 (1996), 3049–3063.Google Scholar
[10]Zhang, J.P., ‘On finite groups all of whose elements of the same order are conjugate in their automorphism groups’, J Algebra 153 (1992), 2236.Google Scholar