@article{Aseeri2024, 
author = {Fawaz Aseeri and Julian Kaspczyk},
title = {The conjugacy diameters of non-abelian finite    p-groups with cyclic maximal subgroups},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {10734-10755},
keywords = {semidihedral group, quaternion group, modular p-groups, normally generating subsets, word norm, conjugacy diameter},
url = {https://www.sciopen.com/article/10.3934/math.2024524},
doi = {10.3934/math.2024524},
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        Conj          G        (      S          ±      1        )  :=  {      h          −      1        s  h      |    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    Δ  (  G  ) for the supremum of all    ‖  G      ‖          S        , where    S is a finite normally generating subset of    G  , and we call    Δ  (  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.}
}