document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182331>Question 1182331</A>: <I><SPAN STYLE=\"word-break: break-all;\">  In permutation group 𝑆6, if 𝛼 = (2 3 4) and 𝛽 = (2 5 6), then find a permutation 𝜙 such that<BR>\n" );
document.write( "𝜙𝛼𝜙<BR>\n" );
document.write( "−1 = 𝛽.<BR>\n" );
document.write( "Let 𝑎 be a fixed element of a ring R, and let<BR>\n" );
document.write( "𝐼𝑠 = {𝑥 ∈ 𝑅 ∶ 𝑠𝑥 = 0}.<BR>\n" );
document.write( "Show that 𝐼𝑠<BR>\n" );
document.write( "is a subring of 𝑅.<BR>\n" );
document.write( "Show that ℤ8 = {0,1,2,3,4,5,6,7,8} is a commutative ring w.r.t. addition modulo 8 and<BR>\n" );
document.write( "multiplication modulo 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812313 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( " </SPAN>\n" );
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