Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By Plato

Thread: Find order of each element

  1. #1
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    681
    Thanks
    1

    Find order of each element

    $\text{Find order of each element, find the generator ($\delta$) of any properties}\\$
    $\displaystyle \displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}
    $
    ok I just started this subject
    is order the number of elements
    but the question was ???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,880
    Thanks
    2890
    Awards
    1

    Re: Find order of each element

    Quote Originally Posted by bigwave View Post
    $\text{Find order of each element, find the generator ($\delta$) of any properties}\\$
    $\displaystyle \displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}$
    ok I just started this subject , is order the number of elements. but the question was ???
    I think that you must give much more of a context in which you find this question/
    The notation $Z_q^*$ suggests this is a subset of a group in the integers with the operation multiplication$\mod(q)~?"$.
    However, that guess really makes very little sense.

    So please please give more context and/or definitions.
    Thanks from bigwave
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    681
    Thanks
    1

    Re: Find order of each element

    Find order of each element-pb1.jpg
    this was the note I tried to copy

    yeah not sure the about the notation its probably just the ussual
    the * might an x and q a 9

    probably I just need to know what to look for.

    I spent an hour surfing the net but...
    Last edited by bigwave; May 24th 2018 at 05:42 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,880
    Thanks
    2890
    Awards
    1

    Re: Find order of each element

    Quote Originally Posted by bigwave View Post
    $\text{Find order of each element, find the generator ($\delta$) of any properties}\\$
    $\displaystyle \displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}$
    ok I just started this subject is order the number of elements but the question was ???
    Quote Originally Posted by bigwave View Post
    Click image for larger version. 

Name:	pb1.jpg 
Views:	6 
Size:	363.3 KB 
ID:	38758
    this was the note I tried to copy yeah not sure the about the notation its probably just the ussual
    the * might an x and q a 9
    probably I just need to know what to look for.
    Well $q=9$ makes a hell of a lot more sense!

    As always $\mathscr{O}{(1)}=1$
    $\mathscr{O}{(2)}=6$ because $2^6\equiv 1\mod(9)$

    Now you show us the rest: $\mathscr{O}{(4)}=?$, $\mathscr{O}{(5)}=?$, $\mathscr{O}{(7)}=?$, $\mathscr{O}{(8)}=?$,
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,571
    Thanks
    1437

    Re: Find order of each element

    It is the multiplicative group of $\mathbb{Z}_9$.

    $2^1\equiv 2 \pmod{9} $
    $2^2\equiv 4 \pmod{9} $
    $2^3\equiv 8 \pmod{9} $
    $2^4\equiv 7 \pmod{9} $
    $2^5\equiv 5 \pmod{9} $
    $2^6\equiv 1 \pmod{9} $

    The order of an element is the smallest positive integer power of the element that gives the identity element (1 in a multiplicative group). For 2 in this group, the smallest such power is 6.
    Last edited by SlipEternal; May 24th 2018 at 06:44 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. element of order II, in 2n order group
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: Dec 14th 2011, 09:32 AM
  2. Order of a Group, Order of an Element
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Nov 15th 2010, 06:28 PM
  3. Order of a Group, Order of an Element
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Nov 15th 2010, 06:02 PM
  4. Find order of this element
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: Oct 6th 2010, 02:00 AM
  5. Order of element
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Nov 4th 2009, 04:10 PM

/mathhelpforum @mathhelpforum