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Locally finite groups with finitely many isomorphism classes of derived subgroups. (English) Zbl 1294.20049
Authors’ summary: Groups which have at most \(n\) isomorphism classes of derived subgroups (\(D_n\)-groups) are studied. A complete classification of locally finite \(D_3\)-groups into nine types is obtained.

MSC:
20F50 Periodic groups; locally finite groups
20F14 Derived series, central series, and generalizations for groups
20E34 General structure theorems for groups
20E25 Local properties of groups
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[1] Berkovich, Y.; Janko, Z., Groups of prime power order, vol. 3, (2012), de Gruyter Berlin
[2] de Giovanni, F.; de Mari, F., Groups with finitely many derived subgroups of non-normal subgroups, Arch. Math. (Basel), 86, 310-316, (2006) · Zbl 1100.20030
[3] de Giovanni, F.; Robinson, D. J.S., Groups with finitely many derived subgroups, J. Lond. Math. Soc. (2), 71, 658-668, (2005) · Zbl 1084.20026
[4] Herzog, M.; Longobardi, P.; Maj, M., On the number of commutators in groups, (Ischia Group Theory 2004, Contemp. Math., vol. 402, (2006), Amer. Math. Soc. Providence, RI), 181-192 · Zbl 1122.20017
[5] Lewis, M., Generalizing camina groups and their character tables, J. Group Theory, 12, 209-218, (2008) · Zbl 1166.20007
[6] Longobardi, P.; Maj, M.; Robinson, D. J.S.; Smith, H., On groups with two isomorphism classes of derived subgroups, Glasg. Math. J., (2013), in press · Zbl 1287.20046
[7] Macdonald, I. D., Some p-groups of Frobenius and extra-special type, Israel J. Math., 40, 350-364, (1981) · Zbl 0486.20016
[8] Newman, M. F., On a class of metabelian groups, Proc. Lond. Math. Soc. (3), 10, 354-364, (1960) · Zbl 0099.25202
[9] Robinson, D. J.S., Finiteness conditions and generalized soluble groups, vol. 2, (1972), Springer Berlin · Zbl 0243.20033
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