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It can be shown that a finite p-group with this property (every abelian subgroup is cyclic) is either cyclic or a generalized quaternion group as defined above. [12] Another characterization is that a finite p-group in which there is a unique subgroup of order p is either cyclic or a 2-group isomorphic to generalized quaternion group. [13]
Thus the multiplicative group of nonzero quaternions acts by conjugation on the copy of consisting of quaternions with real part equal to zero. Conjugation by a unit quaternion (a quaternion of absolute value 1) with real part cos( φ ) is a rotation by an angle 2 φ , the axis of the rotation being the direction of the vector part.
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The World Canine Federation recognizes 350 unique dog breeds. In the U.S. The American Kennel Club now recognizes 209 breeds. That’s…a lot of dogs. To better understand each breed, humans have ...
Despite another short swabbing session, Wisdom Panel successfully identified “Pumpkin” as being Daisy’s twin or the same dog. It identified seven different breeds (German shepherd ...
The character table does not in general determine the group up to isomorphism: for example, the quaternion group Q and the dihedral group of 8 elements, D 4, have the same character table. Brauer asked whether the character table, together with the knowledge of how the powers of elements of its conjugacy classes are distributed, determines a ...
Conformation in dogs refers solely to the externally visible details of a dog's structure and appearance, as defined in detail by each dog breed's written breed standard. [1] [2] [3] A dog that conforms to most of the items of description in its individual breed standard is said to have good conformation.
Additionally, 10 dogs had to be owned by parent club members earning Certificate of Merit (CM) titles. The Lancashire heeler earned recognition from the U.K.'s The Kennel Club in 1981.