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Czechoslovak Mathematical Journal, Vol. 74, No. 4, pp. 955-974, 2024

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

Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand

Received May 24, 2023.   Published online October 28, 2024.
Abstract:  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.
Keywords:  commutativity-preserving exterior product; ${\widetilde{B}_0}$-pairing; curly exterior square; Bogomolov multiplier
Classification MSC:  13A50, 14E08, 14M20, 20D15
DOI:  10.21136/CMJ.2024.0245-23
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Affiliations:   Zeinab Araghi Rostami (corresponding author), Mohsen Parvizi, Department of Pure Mathematics, Ferdowsi University of Mashhad, Azadi Square, 9177948974 Mashhad, Razavi Khorasan Province, Iran, e-mail: araghirostami@gmail.com, zeinabaraghirostami@stu.um.ac.ir, parvizi@um.ac.ir; Peyman Niroomand, School of Mathematics and Computer Science, Damghan University, Semnan Province, Damghan, Iran, e-mail niroomand@du.ac.ir, p_niroomand@yahoo.com
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