linzedun Posted November 11, 2004 Share Posted November 11, 2004 Let H be a normal subgroup of G and let a belong to G. If the element aH has order 3 in the group G/H and H has order 10, what are the possibilities for the order of a? Link to comment Share on other sites More sharing options...
matt grime Posted November 11, 2004 Share Posted November 11, 2004 a^3 is an element of H, an element of H has what possible orders? Link to comment Share on other sites More sharing options...
linzedun Posted November 11, 2004 Author Share Posted November 11, 2004 so the possible orders would be 1, 2, 5, 10? Link to comment Share on other sites More sharing options...
matt grime Posted November 12, 2004 Share Posted November 12, 2004 the possible orders of elements of H are indeed 1,2,5,10, so a^3 has possible orders 1,2,5,10 and hence a has possible order..? Link to comment Share on other sites More sharing options...
linzedun Posted November 13, 2004 Author Share Posted November 13, 2004 3, 6, 15, 30? Link to comment Share on other sites More sharing options...
matt grime Posted November 14, 2004 Share Posted November 14, 2004 Yep. Link to comment Share on other sites More sharing options...
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