Two groups can have same number of elements and same multiplication table {isomorphism, group}. For example, group of eight 2x2 matrices with elements 0 and 1 is isomorphic to C4v group of square symmetries. Isomorphism and homomorphism are independent group properties.
Mathematical Sciences>Group Theory>Mathematical Groups>Morphism
3-Group Theory-Mathematical Groups-Morphism
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Date Modified: 2022.0224