Perfect Group

Herausgegeben:Surhone, Lambert M.; Tennoe, Mariam T.; Henssonow, Susan F.

• Broschiertes Buch

Produktbeschreibung

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The smallest (non-trivial) perfect group is the alternating group A5. More generally, any non-abelian simple group is perfect since the commutator subgroup is a normal subgroup with abelian quotient. Conversely, a perfect group need not be simple; for example, the special linear group SL(2,5) (or the binary icosahedral group which is isomorphic to it) is perfect but not simple (it has a non-trivial center containing left(begin{smallmatrix}4 & 0 0 & 4end{smallmatrix}right)). More generally, a quasisimple group (a perfect central extension of a simple group) which is a non-trivial extension (i.e., not a simple group itself) is perfect but not simple; this includes all the insoluble non-simple finite special linear groups SL(n,q) as extensions of the projective special linear group PSL(n,q) (SL(2,5) is an extension of PSL(2,5), which is isomorphic to A5).

Produktdetails

• Verlag: Betascript Publishing
• Seitenzahl: 92
• Englisch
• Abmessung: 220mm
• ISBN-13: 9786131280511
• ISBN-10: 6131280517
• Artikelnr.: 30174137