The Amit-Ashurst conjecture for finite metacyclic p-groups

被引:2
|
作者
Camina, Rachel D. [1 ]
Cocke, William L. [2 ]
Thillaisundaram, Anitha [3 ]
机构
[1] Fitzwilliam Coll, Cambridge CB30DG, England
[2] Augusta Univ, Augusta, GA 30901 USA
[3] Lund Univ, Ctr Math Sci, S-22362 Lund, Sweden
关键词
Words; Fibres of word maps; Amit-Ashurst conjecture; Metacyclic p-groups;
D O I
10.1007/s40879-023-00644-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite nilpotent group G is either 0, or at least 1/|G|. Noting the work of Ashurst, we name the generalised Amit conjecture the Amit-Ashurst conjecture and show that the Amit-Ashurst conjecture holds for finite p-groups with a cyclic maximal subgroup.
引用
收藏
页数:13
相关论文
共 50 条
  • [41] A REPLACEMENT THEOREM FOR P-GROUPS AND A CONJECTURE
    THOMPSON, JG
    JOURNAL OF ALGEBRA, 1969, 13 (02) : 149 - &
  • [42] KELLER CONJECTURE FOR CERTAIN P-GROUPS
    CORRADI, K
    SZABO, S
    JOURNAL OF ALGEBRA, 1988, 119 (01) : 213 - 217
  • [43] Conjugacy classes of maximal cyclic subgroups of metacyclic p-groups
    Bianchi, Mariagrazia
    Camina, Rachel
    Lewis, Mark L.
    JOURNAL OF GROUP THEORY, 2022, : 377 - 398
  • [44] Finite p-groups all of whose maximal subgroups either are metacyclic or have a derived subgroup of order ≤ p
    Lihua Zhang
    Yanming Xia
    Qinhai Zhang
    Chinese Annals of Mathematics, Series B, 2015, 36 : 11 - 30
  • [45] GROUPS OF AUTOMORPHISMS OF FINITE P-GROUPS
    BOROVIK, AV
    KHUKHRO, EI
    MATHEMATICAL NOTES, 1976, 19 (3-4) : 245 - 255
  • [46] Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p
    Zhang, Lihua
    Xia, Yanming
    Zhang, Qinhai
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2015, 36 (01) : 11 - 30
  • [47] NOETHER'S PROBLEM FOR CENTRAL EXTENSIONS OF METACYCLIC p-GROUPS
    Michailov, Ivo M.
    Ivanov, Ivan S.
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2015, 37 (03): : 209 - 248
  • [48] Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p
    Lihua ZHANG
    Yanming XIA
    Qinhai ZHANG
    Chinese Annals of Mathematics(Series B), 2015, 36 (01) : 11 - 30
  • [49] Finite morphic p-groups
    Caranti, A.
    Scoppola, C. M.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (10) : 4635 - 4641
  • [50] FINITE VALUATED P-GROUPS
    BEERS, D
    HUNTER, R
    WALKER, E
    LECTURE NOTES IN MATHEMATICS, 1983, 1006 : 471 - 507