Elementary Abelian subgroups in 2-groups whose derived subgroups are Klein 4-groups

Abstract

Let P be a finite 2-group. Let ${\mathcal{A}}_2{(P)}_{\ge 2}$ be a poset consisting of elementary abelian subgroups of rank at least 2. If the derived subgroup $P\prime \cong C_2\times C_2$, we proved the spheres occurring in ${\mathcal{A}}_2{(P)}_{\ge 2}$ all have the same dimension.

Keywords:

• Posets
• subgroup complexes

2020 Mathematics Subject Classification:

• 20Dxx
• 55Pxx

Additional information

Funding

Supported by National Natural Science Foundation of China (Nos. 12171142, 12071117), Youth and Middle-aged Talents project of Hubei Provincial Department of Education (No. Q20221003), and National Key R&D Program of China (No. 2020YFE0204200).