Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable. Hillman, J. A. & Linnell, P. A. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 52(2):237–241, April, 1992.
Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable [link]Paper  doi  abstract   bibtex   
If G is an elementary amenable group of finite Hirsch length h , then the quotient of G by its maximal locally finite normal subgroup has a maximal solvable normal subgroup, of derived length and index bounded in terms of h .
@article{hillman_elementary_1992,
	title = {Elementary amenable groups of finite hirsch length are locally-finite by virtually-solvable},
	volume = {52},
	issn = {0263-6115},
	url = {https://www.cambridge.org/core/product/identifier/S1446788700034376/type/journal_article},
	doi = {10.1017/S1446788700034376},
	abstract = {If G is an elementary amenable group of finite Hirsch length h , then the quotient of G by its maximal locally finite normal subgroup has a maximal solvable normal subgroup, of derived length and index bounded in terms of h .},
	language = {en},
	number = {2},
	urldate = {2020-12-14},
	journal = {Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics},
	author = {Hillman, J. A. and Linnell, P. A.},
	month = apr,
	year = {1992},
	pages = {237--241},
}

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