Displaying similar documents to “On hypercentral groups”

The abelianization of hypercyclic groups

B. Wehrfritz (2007)

Open Mathematics

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Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O 2′ (G).

The divisible radical of a group

B.A.F. Wehrfritz (2009)

Open Mathematics

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We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples than positive results. These counterexamples constitute the substantive part of this paper.