Finally, a valid generalisation of the Third Isomorphism Theorem

Let be a commutative group. Let and be subgroups of . If , then . However, what if ? We will consider the general scenario, where and are any subgroups of , provided is not a proper subgroup of . Then In the case that , we have . I have arrived upon this resultContinue reading “Finally, a valid generalisation of the Third Isomorphism Theorem”

An attempted generalization of the Third Isomorphism Theorem.

I recently posted this question on math.stackexchange.com. The link is this. My assertion was “Let be a group with three normal subgroups and such that . Then . This is a generalization of the Third Isomorphism Theorem, which states that , where .” What was my rationale behind asking this question? Let be a groupContinue reading “An attempted generalization of the Third Isomorphism Theorem.”