The Bogomolov multiplier of groups of order $p^7$ and exponent $p$

Araghi Rostami, Zeinab ; Parvizi, Mohsen ; Niroomand, Peyman

Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 955-974

Abstract (VO)

We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order $p^7$ $(p > 2)$ and exponent $p$. We present a comprehensive classification of these groups, identifying those with nontrivial Bogomolov multipliers and distinguishing them from groups with trivial multipliers. Our analysis not only clarifies the conditions under which the Bogomolov multiplier is nontrivial but also refines existing computational methods, enhancing the process of determining these multipliers for the specified class of $p$-groups.

Détail

DOI : 10.21136/CMJ.2024.0245-23

Classification : 13A50, 14E08, 14M20, 20D15
Keywords: commutativity-preserving exterior product; ${\widetilde {B}_0}$-pairing; curly exterior square; Bogomolov multiplier

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