Abstract Algebra Abstract Algebra Math Forum

September 22nd, 2018, 06:45 PM   #1
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Joined: Jun 2018
From: Brasil

Posts: 20
Thanks: 0 algebraic structures

how to complete the table?

thanks
Attached Images 1.jpg (43.5 KB, 9 views) September 22nd, 2018, 07:36 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,111 Thanks: 2326 Hint: + 0 1 2 3 $\ \$ ------- 0|0 1 2 3 1|1 2 3 0 2|2 3 0 1 3|3 0 1 2 September 22nd, 2018, 07:57 PM #3 Senior Member   Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1475 $c \odot a = e$ $a \odot c \odot a = a \odot e = a$ $(a \odot c) \odot a = a$ $a \odot c = e$ $c \odot b = a$ $a \odot c \odot b = a \odot a$ $e \odot b = a \odot a$ $a \odot a = b$ $b \odot a = c$ $a \odot b \odot a = a \odot c$ $(a \odot b) \odot a = e$ $a \odot b = a^{-1}$ $a \odot b = c$ $b \odot a = c$ $b \odot a \odot a = c \odot a$ $b \odot b = e$ $b \odot c = a \odot a \odot c$ $b \odot c = a \odot e$ $b \odot c = a$ $c \odot c = c \odot a \odot b$ $c \odot c = e \odot b$ $c \odot c = b$ $\begin{array}{clcccc} &| &e &a &b &c \\ \hline \\ e &| &e &a &b &c \\ a &| &a &b &c &e \\ b &| &b &c &e &a \\ c &| &c &e &a &b \end{array}$ $a\odot b = b\odot a = c$ $b \odot c = c \odot b = a$ $a \odot c = c \odot a = e$ $G$ is Abelian September 23rd, 2018, 02:59 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,111 Thanks: 2326 Or, as each row and column must contain a permutation of the four elements, 1st step: e a b c a b $\ \$ e b c c e a b 2nd step: e a b c a b c e b c e a c e a b Tags algebraic, structures Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Roberto 37 Linear Algebra 9 September 17th, 2018 02:22 PM Roberto 37 Linear Algebra 7 September 16th, 2018 07:05 PM Roberto 37 Algebra 1 September 16th, 2018 06:21 AM ManUtdFan333 Computer Science 5 December 8th, 2012 03:00 PM ElMarsh Abstract Algebra 0 November 4th, 2009 05:23 PM

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