As Carmichael notes, all of these groups, except for the alternating group, are subgroups of the affine group on the 4-dimensional space over the 2-element finite field.
32.
They generate a group of order 60, isomorphic to the group of rotations of a regular icosahedron or dodecahedron, and therefore to the alternating group of degree five.
33.
Many more finite simple groups are Hurwitz groups; for instance all but 64 of the alternating groups are Hurwitz groups, the largest non-Hurwitz example being of degree 167.
34.
For example, in this way one proves that for, the alternating group A " n " is impossibility of solving a general algebraic equation of degree in radicals.
35.
He gives PSL ( 2, 11 ) and the alternating group of degree 5 as examples, and of course every alternating group of prime degree is an example.
36.
Six times a week, in alternating groups, they are escorted to the Lexington School for the Deaf / Center for the Deaf, five minutes away in Jackson Heights.
37.
He gives PSL ( 2, 11 ) and the alternating group of degree 5 as examples, and of course every alternating group of prime degree is an example.
38.
During the draw procedure, teams were drawn into alternating groups ( Group A, then Group B, repeating ), and assigned a position within the group by drawing another ball.
39.
The symmetric group on an infinite set does not have an associated alternating group : not all elements can be written as a ( finite ) product of transpositions.
40.
They featured improved compartmentalization; propulsion machinery was laid out on the unit system, with alternating groups of boiler rooms and engine rooms, to prevent immobilization by a single torpedo hit.
