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Abstract Algebra 41: The converse of Lagrange's theorem is not true
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Abstract Algebra 41: The converse of Lagrange's theorem is not true
Abstract: We clarify that the converse of Lagrange's theorem is not true. To be more precise, let G be a finite group. Just because a number divides |G|, the size of G, that does not mean that G has a subgroup of that specified size. For example, the alternating group A_4 has size 12, and 6 divides evenly into 12, but A_4 has no subgroups of size 6.
This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
Abstract: We clarify that the converse of Lagrange's theorem is not true. To be more precise, let G be a finite group. Just because a number divides |G|, the size of G, that does not mean that G has a subgroup of that specified size. For example, the alternating group A_4 has size 12, and 6 divides evenly into 12, but A_4 has no subgroups of size 6.
This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
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