A note on non-metabelian A4-groups

Assume p is a prime and G is a finite p -group. We prove that if G is a non-metabelian A 4 -group, then p 6 ⩽ | G | ⩽ p 9 . Moreover, if p ⩾ 5 , then p 6 ⩽ | G | ⩽ p 8 .

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Bibliographic Details
Published inRicerche di matematica Vol. 73; no. 4; pp. 2209 - 2216
Main Authors Song, Qiangwei, Wang, Yuyun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2024
Subjects
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Finite
groups
Minimal nonabelian subgroups
Metabelian groups
20D15
Regular
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Summary:Assume p is a prime and G is a finite p -group. We prove that if G is a non-metabelian A 4 -group, then p 6 ⩽ | G | ⩽ p 9 . Moreover, if p ⩾ 5 , then p 6 ⩽ | G | ⩽ p 8 .
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-022-00744-y