By Jack H. Smith

ISBN-10: 184176440X

ISBN-13: 9781841764405

Nicknamed the 'Unicorns', the 359th FG used to be one of many final teams to reach within the united kingdom for provider within the ETO with the 8th Air strength. First seeing motion on thirteen December 1943, the crowd at the beginning flew bomber escort sweeps in P-47s, ahead of changing to the ever present P-51 in March/April 1944. all through its time within the ETO, the 359th was once credited with the destruction of 351 enemy airplane destroyed among December 1943 and will 1945. The exploits of all 12 aces created by way of the gang are targeted, in addition to the main major missions flown. This booklet additionally discusses many of the markings worn by way of the group's 3 squadrons, the 368th, 369th and 370th FSs

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All characters of G are real-valued) for if X EO Irr G and X(l) = (jill, then we have 23m. X(g) Ker cp = {Q(O, b)lb = o {q"'),(g) where 1 of=- ), EO Irr Z(G) and ),2 = l. Let C EO LX with ord c = qn1 + 1. Then is an epimorphism of Q onto L + with + b = O} = q {Q(O, b)lb = b q E K}. (x, Therefore Q' ~ Ker cp II) On the number of solutions of y'" = I in a group I in a group = ~ Z(Q). As YY = ifg¢Z(G) if 9 EO Z(G), IX, defined by (ex) y) is an automorphism of G, fixing G' elementwise and operating fixed-pointfreely on GIG'.

A) Let Vi (i = 1,2) be KGi-modules. Then the tensor product VI Q9 K V2 (ouer K) obviously becomes a K(G 1 x G2 )-module by Iij are characters of G1 x G2 by a). lc)r Vi E Vi, rr gi E Gj • is the churacter of Gj is givell by Xj Oil Vi, then the character I of G1 X G2 on V[ Q9 V2 97 Iij Iij(1)2 = are irreducible and distinct. d. 5 for nilpotent groups. 2 Theorem. Let G be nilpotent and 'I b) LeI Xl' ... h be the irreducible characters of Glover C and G2 over C. Then the I jj , defined by irreducihle charocters or l/ll' ...

Hence if D;. is irreducible, then for some a E A. The character Xi. of Di. is given by A, 80 Characters of some small groups Characters of some small groups We define a character ),' of A by ),'(a) = ),(a b ). Hence A i=- ),' and therefore Hence X;. is irreducible. ll such J.. Two characters Xi. and Xu = E A, but Ie rt G,l-. Hence by IA/-IA: G'I are equal if and only if This requires JI = ;. '. I-knce each pair I"~ Ie' provides the same character x;. of G, and we obtain ~(IAI - -> Then Z(G) = E, hence by b) G does not have any faithful irreducible representation.

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