ON FINITE-BY-NILPOTENT PROFINITE GROUPS

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Detomi Eloisa; Morigi Marta

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2020 | Volume:9 | Issue:4 Page(s): 223-229

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Information Journal Paper

Title

ON FINITE-BY-NILPOTENT PROFINITE GROUPS

Author(s)

Detomi Eloisa | Morigi Marta | Issue Writer Certificate

Keywords

Conjucagy classes

verbal subgroups

pro

nite groups

FC-groups

Abstract

Let n = [x1, : : :, xn] be the nth lower central word. Suppose that G is a pro, nite group where the conjugacy classes x n(G) contains less than 2@ 0 elements for any x 2 G. We prove that then n+1(G) has , nite order. This generalizes the much celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is , nite. Moreover, it implies that a pro, nite group G is , nite-by-nilpotent if and only if there is a positive integer n such that x n(G) contains less than 2@ 0 elements, for any x 2 G.

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APA: Copy

Detomi, Eloisa, & Morigi, Marta. (2020). ON FINITE-BY-NILPOTENT PROFINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 9(4), 223-229. SID. https://sid.ir/paper/1003600/en

Vancouver: Copy

Detomi Eloisa, Morigi Marta. ON FINITE-BY-NILPOTENT PROFINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2020;9(4):223-229. Available from: https://sid.ir/paper/1003600/en

IEEE: Copy

Eloisa Detomi, and Marta Morigi, “ON FINITE-BY-NILPOTENT PROFINITE GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 9, no. 4, pp. 223–229, 2020, [Online]. Available: https://sid.ir/paper/1003600/en

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