p-GROUPS WITH CYCLIC OR GENERALISED QUATERNION HUGHES SUBGROUPS: CLASSIFYING TIDY p-GROUPS

被引：1
|
作者：
Beike, Nicolas F. F. [1 ]
Carleton, Rachel [1 ]
Costanzo, David G. G. [2 ]
Heath, Colin [3 ]
Lewis, Mark L. L. [1 ]
Lu, Kaiwen [4 ]
Pearce, Jamie D. D. [5 ]
机构：
[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA
[2] Clemson Univ, Sch Math & Stat Sci, O 110 Martin Hall,POB 340975, Clemson, SC 29634 USA
[3] NYU, Sch Law, 40 Washington Sq South, New York, NY 10012 USA
[4] Brown Univ, Dept Math, Providence, RI 02912 USA
[5] Univ Texas Austin, Dept Math, 2515 Speedway,PMA 8 100, Austin, TX 78712 USA
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2023年 / 108卷 / 03期
基金：
美国国家科学基金会;
关键词：
tidy groups; the Hughes subgroup;
D O I：
10.1017/S000497272300031X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let G be a p-group for some prime p. Recall that the Hughes subgroup of G is the subgroup generated by all of the elements of G with order not equal to p. In this paper, we prove that if the Hughes subgroup of G is cyclic, then G has exponent p or is cyclic or is dihedral. We also prove that if the Hughes subgroup of G is generalised quaternion, then G must be generalised quaternion. With these results in hand, we classify the tidy p-groups.
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页码：443 / 448
页数：6
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