Linear Groups Microform With An Exposition of the Galois Field Theory
Linear Groups Microform With An Exposition of the Galois Field Theory
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Hence CU is the only substitution in addition to U which corresponds to the product W ~ U-JJi= C U^ - CU V It follows that the quotient - group of {U} by {/, C} is holoedrically isomorphic both with the simple linear fractional group LF(2, p'* n ') and with the group {W\ In particular, the order of {W} is JL(jp4_l)p2n or (2 4n l)2 2w according as p > 2 or p = 2. For >> 2, p n > 3, IJ^n has the order (p* n + p n ) (p 2n l}p n, being holo- edrically isomorphic with O v (4, ^) n ), whose order is ...given in 172. For p = 2, jEJ 4) g* is holoedrically isomorphic with the group leaving i%+ 2% + ^i? + ^i absolutely invariant, whose order is shown in 204 to be 2(2 4 -l)2 2w . Hence {W} is of index 2 under E^n. According as p > 2 or p = 2, { W } is extended to E^ p n by T 2, x or (li%), where ^ is any not -square in the GrF[p n ]. It is only necessary to show that these substitutions are not of the form W, If (gj%) were of the form TF, then
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To quickly assess the difficulty of the text, read a short excerpt:
Hence CU is the only substitution in addition to U which corresponds to the product W ~ U-JJi= C U^ - CU V It follows that the quotient - group of {U} by {/, C} is holoedrically isomorphic both with the simple linear fractional group LF(2, p'* n ') and with the group {W\ In particular, the order of {W} is JL(jp4_l)p2n or (2 4n l)2 2w according as p > 2 or p = 2. For >> 2, p n > 3, IJ^n has the order (p* n + p n ) (p 2n l}p n, being holo- edrically isomorphic with O v (4, ^) n ), whose order is ...given in 172. For p = 2, jEJ 4) g* is holoedrically isomorphic with the group leaving i%+ 2% + ^i? + ^i absolutely invariant, whose order is shown in 204 to be 2(2 4 -l)2 2w . Hence {W} is of index 2 under E^n. According as p > 2 or p = 2, { W } is extended to E^ p n by T 2, x or (li%), where ^ is any not -square in the GrF[p n ]. It is only necessary to show that these substitutions are not of the form W, If (gj%) were of the form TF, then
What to read after Linear Groups Microform With An Exposition of the Galois Field Theory?
You can find similar books in the "Read Also" column, or choose other free books by Leonard E Leonard Eugene Dickson to read online
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