Conjectures

December 2001

  1. (BJT conjecture) Every subgroup $H$ of a finite group $G$ which has index 2 in $G$ is a normal subgroup of $G.$
  2. (CEK corollary) The subgroup of all rotations of $D_{n}$ is a normal subgroup of $D_{n}.$
  3. (9-conjecture) The commutator subgroup of any group is normal.
  4. (7-conjecture) The center of any group is normal.
  5. (6-conjecture) Let $n$ be odd, and let $H$ be the commutator subgroup of $D_{n}.$ Then MATH
  6. (DJKT conjecture) Let $n$ be even and let $K$ be the commutator subgroup of $D_{n}.$ Then MATH
  7. (Kevin's conjecture) Let $n$ be even and let MATH be the subgroup of $D_{n}$ consisting of the identity and the 180$^{\circ }$ rotation. Then $C$ is normal in $D_{n}$ and MATH

Students who contributed the conjectures:

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