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On elementary amenable groups of finite Hirsch number

  • B. A. F. Wehrfritz (a1)

Abstract

We give an alternative short proof of a recent theorem of J. A. Hillman and P.A. Linnell that an elementary amenable group with finite Hirsch number has, modulo its locally finite radical, a soluble normal subgroup with index and derived length bounded only in terms of the Hirsch number of the group.

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References

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[1]Hillman, J. A., ‘Elementary amenable groups and 4-manifolds with Euler characterictic O’, J. Austral. Math. Soc. (Series A) 50 (1991), 160170.
[2]Hillman, J. A. and Linnell, P. A., ‘Elementary amenable groups of finite Hirsch length are locally-finite by virtually-solvable’, J. Austral. Math. Soc. (Series A) 52 (1992), 237241.
[3]Kegel, O. H. and Wehrfritz, B. A. F., Locally finite groups (North-Holland, Amsterdam, 1973).
[4]Mal'cev, A. I., ‘On certain classes of infinite soluble groups’, Mat. Sb. 28 (1951), 567588 (in Russian)
Amer. Math. Soc. Transl. Ser. 2 Vol. 2 (1956), 121.
[5]Robinson, D. J. S., Finiteness conditions and generalized soluble groups 2 (Springer, Berlin, 1972).
[6]Wehrfritz, B. A. F., Infinite linear groups (Springer, Berlin, 1973).
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On elementary amenable groups of finite Hirsch number

  • B. A. F. Wehrfritz (a1)

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