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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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    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