The Bogomolov multiplier of groups of order p⁷ and exponent p

We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order p⁷ (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.