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Thread: elements in a general product

  1. #1
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    elements in a general product

    Let A,B be two subgroups of G where only A is normal.
    If x \notin AB, does it mean that x \notin A and x \notin B?
    Suppose x \notin AB and  y \notin A. Does it implies xy \notin A?
    Last edited by deniselim17; Nov 9th 2017 at 03:55 AM.
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  2. #2
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    Re: elements in a general product

    First question

    A\subseteq \text{AB}

    therefore

    \text {if } x \notin\text {AB }\text {then } x \notin A

    Second question

    consider A=B=<e> the trivial group
    Last edited by Idea; Nov 9th 2017 at 07:21 AM.
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  3. #3
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    Re: elements in a general product

    if x \notin A, x \notin B, does it mean that x \notin AB?
    A is normal subgroup of G.
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  4. #4
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    Re: elements in a general product

    Quote Originally Posted by deniselim17 View Post
    if x \notin A, x \notin B, does it mean that x \notin AB?
    A is normal subgroup of G.
    No

    Definition: \text{AB}=\{a b : a\in A, b\in B\} Correct?
    Last edited by Idea; Nov 13th 2017 at 04:20 AM.
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