Fill in multiplication tables to discover and understand finite groups. Master the art of abstract algebra through interactive exploration!
1. Exploration Mode: Freely create and explore group structures to discover new groups. This is where you learn and experiment!
2. Gallery: View all groups you've discovered in exploration mode. Your personal collection of mathematical achievements.
3. Puzzle Mode: Solve challenging puzzles based on groups you've already discovered. Test your understanding!
• Click a cell to select it
• Type numbers (0-9) to fill values
• Backspace/Delete to clear a cell
• Right-click to quickly clear
• Click headers to swap elements (powerful tool!)
• ESC to return to menu
Closure: All products must be in the group (no values outside 0 to n-1)
Associativity: (a·b)·c = a·(b·c) for all elements
Identity: There exists e such that e·a = a·e = a for all a
Inverses: For each a, there exists b such that a·b = b·a = e
• Start with the identity: Find which element acts as the identity first
• Latin square property: Each row and column must contain all elements exactly once
• Use element swapping: Click headers to standardize your table - this is crucial for puzzle solving!
• Study patterns: Pay attention to element orders and conjugacy classes
• Exploration first: Discover groups in exploration mode before attempting puzzles
• Small groups are easier: Start with order 4 to understand the basics