There is a bewildering number of " accidental " isomorphisms between various small groups of Lie type ( and alternating groups ).
22.
The only composition series of is } ( where is the alternating group on five letters, also known as the icosahedral group ).
23.
The even permutations produce the subgroup of permutation matrices of determinant + 1, the order " n " ! / 2 alternating group.
24.
For example, for the alternating group, } }, the outer automorphism group is usually the group of order 2, with exceptions noted below.
25.
The original book was a sketchbook made up of alternating groups of white and blue pages, in fours, with an average page size of.
26.
In this case the alternating group agrees with the symmetric group, rather than being an index 2 subgroup, and the sign map is trivial.
27.
For example, the groups SL ( 2, 4 ), PSL ( 2, 5 ), and the alternating group on 5 points are all isomorphic.
28.
He found that in some materials, alternating groups of atoms align their electrons in opposite directions, neutralizing the net magnetic effect, the phenomenon called antiferromagnetism.
29.
The alternating groups usually have an outer automorphism group of order 2, but the alternating group on 6 points has an Schur multiplier of order 6.
30.
The alternating groups usually have an outer automorphism group of order 2, but the alternating group on 6 points has an Schur multiplier of order 6.
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