A146992 Numbers n with the property that there exists a group of order n in which some element of the commutator subgroup G' is not a commutator [x,y].

96, 128, 144, 162, 168, 192, 216, 240, 256, 270, 288, 312, 320, 324, 336, 360, 378, 384, 400, 432, 448, 450, 456, 480, 486, 504, 512, 528, 540, 560, 576, 594, 600, 624, 640, 648, 672, 702, 704, 720, 729, 744, 750, 756, 768, 784, 792, 800, 810, 816, 832, 840

Offset: 1

Author

Bob Heffernan and Des MacHale, Nov 04 2008

Keywords

• hard
• nonn

Comments

Every multiple of a(n) is also a term of the sequence because the direct product of a group G with any Abelian group A satisfies (GXA)' = G'.

Examples

			a(1) = 96 because there is a group G of order 96 in which an element of G' is not a commutator.