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Solution of Polynomials by Real RadicalsAuthor(s): I. M. IsaacsSource: The American Mathematical Monthly, Vol. 92, No. 8 (Oct., 1985), pp. 571-575Published by: Mathematical Association of AmericaStable URL: http://www.jstor.org/stable/2323164.
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8/12/2019 extensiones (1)
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1985]
NOTES
571
Acknowledgement.
he authorwishes
o thankN. Linial forhis
helpful emarks uring n early
presentation
f
this ubject
n
Jerusalem,
982.
References
1. R. L. Graham and H. 0. Pollak, On the addressing
roblemfor oop switching, ell SystemTech. J., 50
(1971), 2495-2519; see also
On
embedding raphs
n
squashed cubes ,
n
Graph Theory nd its Applications,
.
Alavi et al. ed., LectureNotes
in
Math., Springer-Verlag,
ol. 303
(1972) 99-110.
2. J. Kasem, Ph.D. Thesis,HebrewUniversity,
erusalem,984.
3.
G.
W.
Peck,
New
proof
f a theorem f Graham and Pollak,DiscreteMath.,49 (1984)
327-328.
4. B. Reznick,P. Tiwari, nd
D. B.
West,
Decomposition f productgraphs nto complete ipartite ubgraphs,
U.
of
Illinois,Urbana,
1984.
5. H. Tverberg, n
the
decomposition
f
K,,
intocomplete ipartite raphs, .Graph Theory, (1982) 493-494.
6. J. Zaks, Bounds
of
neighborly
amilies f convex
polytopes,
eom.
Dedicata,
8
(1979)
279-296.
NOTES
EDITED BY SABRA
S.
ANDERSON,
SHELDON AXLER, AND
J.ARTHUR
SEEBACH,
JR.
For nstructions
bout ubmittingotes or
ublicationn this epartmentee the nside ront over.
SOLUTION
OF
POLYNOMIALS BY
REAL
RADICALS*
I. M.
ISAACS
DepartmentfMathematics, niversityf Wisconsin,
adison,WI 53706
Let
F
be a field nd letf
E
F[x]
be a polynomial. ecall thatf
is
said to be solvable y
radicals
if
f splits ver
ome xtension ield
E
D
F
forwhich here
xists
chain f fields
F=
Fo
cF,
c
...
c
Fk
=
E
suchthat
J,
=
-
1[i
]
for1