Recent content by physix123

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    Graduate How to Find the Subgroup of a Quotient Group with a Given Generator?

    i am confused about how to find the subgroup of a quotient group given a generator. for example, a lot of problems give as the group Z/nZ with n very large. how do you find the subgroup given a generator? thanks!
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    Graduate Proving Non-Isomorphism: Subgroup and Dihedral Group of Equal Order

    how would you go about showing that a subgroup and dihedral group- of the same order- are not isomorphic?
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    Undergrad Can a permutation with non-disjoint cycles still be used to find its order?

    i am pretty sure it's true that to find the order of a permutation, you can find LCM of the length of the disjoint cycles... if you have a permutation that doesn't have disjoint cycles (i.e. like one with (1,3,6,8)(4,6)), then can you use the same method to find the order? I feel like I am...