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Finite groups in which some property of two-generator subgroups is transitive

  • Costantino Delizia (a1), Primoz Moravec (a2) and Chiara Nicotera (a3)

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Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.

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References

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[1]Delizia, C., Moravec, P., and Nicotera, C., ‘Groups in which the bounded nilpotency of two-generator subgroups is a transitive relation’, Beiträge Algebra Geom. (to appear).
[2]Huppert, B., Endliche gruppen (Springer-Verlag, Berlin, 1967).
[3]Huppert, B. and Blackburn, N., Finite groups III (Springer-Verlag, New York, 1982).
[4]Lennox, J.C., ‘Bigenetic properties of finitely generated hyper-(abelian-by-finite) groups’, J. Austral. Math. Soc. 16 (1973), 309315.
[5]Robinson, D.J.S., (Part 1), Finiteness conditions and generalized soluble groups (Springer-Verlag, Berlin, 1972).
[6]Suzuki, M., ‘The nonexistence of certain type of simple groups of odd order’, Proc. Amer. Math. Soc. 8 (1957), 686695.
[7]Suzuki, M., ‘Finite groups with nilpotent centralizers’, Trans. Amer. Math. Soc. 99 (1961), 425470.
[8]Suzuki, M., ‘On a class of doubly transitive groups’, Ann. of Math. 75 (1962), 105145.
[9]Thompson, J.G., ‘Non-solvable finite groups all whose local subgroups are solvable’, Bull. Amer. Math. Soc. 74 (1968), 383437.
[10]Weisner, L., ‘Groups in which the normaliser of every element except identity is abelian’, Bull. Amer. Math. Soc. 31 (1925), 413416.
[11]Wu, Y.F., ‘Groups in which commutativity is a transitive relation’, J. Algebra 207 (1998), 165181.
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Finite groups in which some property of two-generator subgroups is transitive

  • Costantino Delizia (a1), Primoz Moravec (a2) and Chiara Nicotera (a3)

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