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A complete classification of finite homogeneous groups

  • Cai Heng Li (a1)

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In this short note, we obtain a complete classification of finite homogeneous groups.

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References

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[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).
[2]Cherlin, G.L. and Felgner, U., ‘Quantifier eliminable groups’, in Logic Colloquium 1980, (van Dalen, , Editor) (North-Holland, Amsterdam, 1982), pp. 6981.
[3]Cherlin, G.L. and Felgner, U., ‘Homogeneous solvable groups’, J. London Math. Soc. (2) 44 (1991), 102120.
[4]Feit, W. and Seitz, G.M., ‘On finite rational groups and related topics’, Illinois J. Math. 33 (1989), 103131.
[5]Li, C.H., ‘Isomorphisms of finite Cayley digraphs of bounded valency II’, J. Combin. Theory Ser. A (to appear).
[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.
[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.
[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.
[9]Stroth, G., ‘Isomorphic subgroups’, Comm. Algebra 24 (1996), 3049–3063.
[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.
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A complete classification of finite homogeneous groups

  • Cai Heng Li (a1)

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