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A class of groups rich in finite quotients
Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 263-274

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If X is a class of groups, the class of counter-Xgroups is defined to consist of all groups having no non-trivial X-quotients. The counter-abelian groups are the perfect groups and the counter-counter-abelian groups are the imperfect groups studied by Berrick and Robinson [2]. This paper is concerned with the class of counter-counterfinite groups. It turns out that these are the groups in which any non-trivial quotient has a non-trivial representation over any finitely generated domain (Theorem 1.1), so we shall call these groups highly representable or HR-groups. 
Walter, Vonn. A class of groups rich in finite quotients. Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 263-274. doi: 10.1017/S0017089500031694
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[1] 1.Arnold, D. M., Finite Rank Torsion Free Abelian Croups and Rings (Springer, Berlin, 1982). Google Scholar | DOI

[2] 2.Berrick, A. J. and Robinson, D. J. S., Imperfect groups, J. Pure Appl. Algebra 88 (1993), 3–22. Google Scholar | DOI

[3] 3.Fuchs, L., Infinite Abelian Groups, 2 vols. (Academic Press, New York, 1970/1973). Google Scholar

[4] 4.Gruenberg, K. W., Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. Google Scholar | DOI

[5] 5.Hall, P., The Edmonton Notes on Nilpotent Groups (Queen Mary College Mathematics Notes, 1969). Google Scholar

[6] 6.Hickin, K. K., Complete universal locally finite groups, Trans. Amer. Math. Soc. 239 (1978), 213–227. Google Scholar | DOI

[7] 7.Kuroš, A. G., The Theory of Groups, 2nd ed., vol. 2 (Chelsea, New York, 1960). Google Scholar

[8] 8.Robinson, D. J. S., Finiteness Conditions and Generalized Solvable Groups, 2 vols., (Springer, Berlin, 1972). Google Scholar

[9] 9.Robinson, D. J. S., A Course in the Theory of Groups (Springer, New York, 1980). Google Scholar

[10] 10.Rose, J. S., A Course on Group Theory (Cambridge University Press, 1978). Google Scholar

[11] 11.Scott, W. R., Group Theory (Prentice-Hall, Englewood Cliffs, NJ, 1964). Google Scholar

[12] 12.Warfield, R. B., Nilpotent Groups (Springer, Berlin, 1976). Google Scholar | DOI

[13] 13.Wehrfritz, B. A. F., Infinite Linear groups (Springer, Berlin, 1973). Google Scholar | DOI

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