Dihedral Groups : Group Action

Related BrainMass Solutions

• Dihedral Groups

  Dihedral Groups are investigated.

• Groups of Order 18

  There are the following. 1) Cartesian product S_3 x C_3, Symmetric group of order 3 with Cyclic group of order 3. 2) D_9, the Dihedral group of order 18. 3) G_18 (3), the semidirect product of C_3 x C_3 with C_2 with group presentation x,y,

• Isomorphic groups

  Decide which (if any) of the following are isomorphic to which: (a) D3xS4 (b) D6xA4 (c) D4xD9 Dn=dihedral group of order 2n, An=alternating group of degree n, Sn=symmetric group of degree n GxH=internal direct product of G and H please see attached

• Algebraic Structures : Quaternions and Dihedral Groups

  Quaternions and dihedral groups are investigated.

• Definitions of Equivalence & Groups

  A non-abelian group not commutative. In non-abelian groups, the order in which the binary operation is performed matters. Examples: matrices under multiplication, the group of symmetries of a square (D8), the dihedral group (D3).

• Definitions and Examples : Groups, Abelian Groups and Non-Abelian Groups

  simplest non-Abelian group is the dihedral group D3, which is of group order six.

• Problems in Group Theory and Quaternions

  We solve three problems involving quaternions as well as dihedral and cyclic groups.

• Semidirect product

  attached This provides an example of proving a dihedral group is a semidirect product and a quaternion group is not.

• Stereochemistry of the Addition of Bromine to Trans-Cinnamic Acid

  Highlight the Br-C-C-Br dihedral angle. Is the diehdral angle (0 degrees for sin addition or 180 degrees for anti addition)? Look at the dihedral angle between the phenyl ring and the carboxylic acid group.