We consider groups G such that the set [G, phi] = {g(-1) g(phi)|g is an element of G} is a subgroup for every automorphism phi of G, and we prove that there exists such a group G that is finite and nilpotent of class n for every n is an element of N. Then there exists an infinite not nilpotent group with the above property and the Conjecture 18.14 of Khukhro and Mazurov (The Kourovka Notebook No. 20, 2022) is false.
On finite groups in which the twisted conjugacy classes of the unit element are subgroups
Nicotera C.
2024-01-01
Abstract
We consider groups G such that the set [G, phi] = {g(-1) g(phi)|g is an element of G} is a subgroup for every automorphism phi of G, and we prove that there exists such a group G that is finite and nilpotent of class n for every n is an element of N. Then there exists an infinite not nilpotent group with the above property and the Conjecture 18.14 of Khukhro and Mazurov (The Kourovka Notebook No. 20, 2022) is false.File in questo prodotto:
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