Given a group G, we write x^G for the conjugacy class of G containing the element x. A famous theorem of B. H. Neumann states that if G is a group in which all conjugacy classes are finite with bounded size, then the derived group G′ is finite. We establish the following result. Let n be a positive integer and K a subgroup of a group G such that |x^G| ≤ n for each x ∈ K. Let H=⟨K^G⟩ be the normal closure of K. Then the order of the derived group H′ is finite and n-bounded. Some corollaries of this result are also discussed.

A stronger form of Neumann's BFC-theorem / Acciarri, C; Shumyatsky, P. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 242:1(2021), pp. 269-278. [10.1007/s11856-021-2133-1]

A stronger form of Neumann's BFC-theorem

Acciarri C;
2021

Abstract

Given a group G, we write x^G for the conjugacy class of G containing the element x. A famous theorem of B. H. Neumann states that if G is a group in which all conjugacy classes are finite with bounded size, then the derived group G′ is finite. We establish the following result. Let n be a positive integer and K a subgroup of a group G such that |x^G| ≤ n for each x ∈ K. Let H=⟨K^G⟩ be the normal closure of K. Then the order of the derived group H′ is finite and n-bounded. Some corollaries of this result are also discussed.
2021
242
1
269
278
A stronger form of Neumann's BFC-theorem / Acciarri, C; Shumyatsky, P. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 242:1(2021), pp. 269-278. [10.1007/s11856-021-2133-1]
Acciarri, C; Shumyatsky, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1255510
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