The conjugacy diameters of non-abelian finite p-groups with cyclic maximal subgroups

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

Let G be a group. A subset S of G is said to normally generate G if G is the normal closure of S in G. In this case, any element of G can be written as a product of conjugates of elements of S and their inverses. If g ∈ G and S is a normally generating subset of G, then we write ‖g‖S for the length of a shortest word in ConjG (S±1):= {h−1 sh|h ∈ G, s ∈ S or s−1 ∈ S } needed to express g. For any normally generating subset S of G, we write ‖G‖S = sup{‖g‖S | g ∈ G}. Moreover, we write ∆(G) for the supremum of all ‖G‖S, where S is a finite normally generating subset of G, and we call ∆(G) the conjugacy diameter of G. In this paper, we derive the conjugacy diameters of the semidihedral 2-groups, the generalized quaternion groups and the modular p-groups. This is a natural step after the determination of the conjugacy diameters of dihedral groups.

Details

OriginalspracheEnglisch
Seiten (von - bis)10734-10755
Seitenumfang22
FachzeitschriftAIMS mathematics
Jahrgang9
Ausgabenummer5
PublikationsstatusVeröffentlicht - 2024
Peer-Review-StatusJa

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • conjugacy diameter, modular p-groups, normally generating subsets, quaternion group, semidihedral group, word norm