Determination of the Abstract Groups of Order 16 Psuperscript 2 And 8 Psupers
Determination of the Abstract Groups of Order 16 Psuperscript 2 And 8 Psupers
Ragnar Nyhln
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Two types for which a=^ = d and y = d or d^ (2) a and /^ the prim, roots of ^*=1, y = + 1. Four types for which a = d and fi = d or d^ (3) a the prim, roots of ^^=1, /? and y= + 1. Three types for which a = dj /?= + !, y=l and a = 6, fi = y = —l H=E '. ' a^ = p» = y»=l (1) a, /? and y the prim, roots of ^8 = 1. Five types for which a = p = d, y = d'-(r=l, 3, 5, 7) and a = d, P = d^, y = d^ (2) a and /? the prim, roots of 6^ = 1, y=± 1, ^* or d^. Fourteen types for which a = d, p = d^(r = 1, 3, ...5, 7), / = ± 1 or ^2 and a = ^, /S = ^'"(r = 1, 5), y = d^ (3) a the prim, roots of 6^ = 1, p and y = ± 1, d- or ^^^ Three types for which a = dy P = d^, y = d^{r = 2, 6) and a = dy p = y = d^. Seven types for which a = d, p = d^{r - = 0, 2, 4, 6), y= ± 1 (except p = -y=\). (ii) r = 1 We can choose J^ = (Pi, F^y Pg, P^ Pg, P^^F^^P^^ If Pg is transformed into an operation in {Pj, Pg) we are brought back to the previous case. The permutation of all Gp except {P^} corresponding to the isomorphism J a contains cycles with 2, 4 or 8 tenns.
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