Question
1. Let M be an abelian group and D a subgroup. For any element m of M, where m has order 2, define mD={md│d∈D}. Prove that the set C=D∪mD is a subgroup of M.
Solution     Reflective Narrative

2. Suppose M and D are isomorphic groups. Prove that Aut(M) is isomorphic to Aut(D).
Solution     Reflective Narrative

3. Let C be a group with |C| = 44. Prove that C must contain an element of order 2.
Solution    Reflective Narrative

8. An abstract algebra teacher intended to give a typist a list of nine integers that form a group under multiplication modulo 91. Instead, one of the nine integers was inadvertently left, out, so that the list appeared as 1, 9, 16, 22, 53, 74, 79, 81. Which integer was left out? (This really happened!
Solution    Reflective Narrative
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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