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On central automorphisms of finite-by-nilpotent groups

  • Silvana Franciosi (a1) and Francesco de Giovanni (a2)

Abstract

The effect of imposing a certain finiteness condition on the group of central automorphisms of a finite-by-nilpotent group is investigated. In particular it is shown that, if each central automorphism of a finite-by-nilpotent group G has finite order, then the factor group G/Z(G) has finite exponent.

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References

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1.Curzio, M., Robinson, D. J. S., Smith, H. and Wiegold, J., Some remarks on central automorphisms of hypercentral groups, Arch. Math. (Basel), to appear.
2.Franciosi, S. and De Giovanni, F., A note on groups with countable automorphism groups, Arch. Math. (Basel) 47 (1986), 1216.
3.Franciosi, S., De Giovanni, F. and Robinson, D. J. S., On torsion in groups whose automorphism groups have finite rank, Rocky Mountain J. Math. 17 (1987), 431445.
4.Fuchs, L., Infinite Abelian Groups (Academic Press, New York-London, 19701973).
5.Hall, M. Jr., The Theory of Groups (MacMillan, New York, 1959).
6.Lennox, J. C. and Robinson, D. J. S., Soluble products of nilpotent groups, Rend. Sem. Mat. Univ. Padova 62 (1980), 261280.
7.Pettet, M. R., Locally finite groups as automorphism groups, Arch. Math. (Basel) 48 (1987), 19.
8.Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups (Springer, Berlin, 1972).
9.Robinson, D. J. S., The vanishing of certain homology and cohomology groups, J. Pure Appl. Algebra 7 (1976), 145176.
10.Robinson, D. J. S., A contribution to the theory of groups with finitely many automorphisms, Proc. London Math. Soc. (3) 35 (1977), 3454.
11.Robinson, D. J. S., Homology of group extensions with divisible abelian kernel, J. Pure Appl. Algebra 14 (1979), 145165.
12.Robinson, D. J. S., Infinite torsion groups as automorphism groups, Quart. J. Math. Oxford (2) 30 (1979), 351364.
13.Robinson, D. J. S., On the homology of hypercentral groups, Arch. Math. (Basel) 32 (1979), 223226.
14.Stammbach, U., Homology in Group Theory (Lecture Notes in Mathematics 359, Springer, Berlin, 1973).
15.Zimmerman, J., Countable torsion FC-groups as automorphism groups, Arch. Math. (Basel) 43 (1984), 108116.

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