document.write( "Question 1137638: Write True if the statement is correct, Otherwise write FALSE.In each case give a brief explanation.
\n" ); document.write( "1. Every abelian group is cyclic.
\n" ); document.write( "2. If H and K are subgroups of a group G, then H intersects K is a group.
\n" ); document.write( "3. Every permutation is a cycle.
\n" ); document.write( "4. Every function is a permutation if and only if it is one-to-one.
\n" ); document.write( "5. Every group, has a unique generator. \r
\n" ); document.write( "\n" ); document.write( "Hi The Best Teachers online! Can you help me on this question please? Thank you! God bless! \n" ); document.write( "

Algebra.Com's Answer #755488 by ikleyn(52863) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " I will give only short answers of the type \"TRUE\"/\"FALSE\".\r
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document.write( "1.  FALSE.\r\n" );
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document.write( "    Counter-examples:\r\n" );
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document.write( "        a)  Abelian groups that are direct sums of other abelian groups, are not cyclic.\r\n" );
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document.write( "        b)  The additive group of all real numbers is not cyclic.\r\n" );
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document.write( "        c)  The multiplicative group of all positive real numbers is not cyclic.\r\n" );
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document.write( "2.  TRUE.\r\n" );
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document.write( "    Make a proof on your own.\r\n" );
document.write( "    It is easy.\r\n" );
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document.write( "3.  \r\n" );
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document.write( "4.  TRUE.\r\n" );
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document.write( "    If it is the function on discrete finite set, mapping it on itself.\r\n" );
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document.write( "5.  FALSE.\r\n" );
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document.write( "    Counter-examples:\r\n" );
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document.write( "        a)  Abelian groups that are direct sums of other abelian groups, are not cyclic.\r\n" );
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document.write( "        b)  The additive group of all real numbers is not cyclic.\r\n" );
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document.write( "        c)  The multiplicative group of all positive real numbers is not cyclic.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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