A set theoretic version of equations on groups

Key Points

• This paper aims to explore the number of solutions to a specific equation defined on finite groups.
• Studied finite groups G with respect to solutions S that satisfy $$℧^{\{n\}}(S)=L$$.
• Considered special cases such as normal subsets, abelian groups, and extraspecial p-groups.
• Utilized set theoretic approaches to analyze the structure and solutions.
• Identified conditions under which the equation has solutions.
• Outlined distinct findings for normal subsets and specific group types.
• Provided insights into the behavior of the solutions based on group properties.