Advertisement

Character and conjugacy class hypergroups of a finite group

  • 71 Accesses

  • 15 Citations

Summary

An axiomatization of abelian hypergroups is given which allows for factor hypergroups to be developed. The hypergroup of characters and the hypergroup of conjugacy classes of a finite group are studied and compared. It is seen (using a theorem of Clifford) that if K is a normal subgroup of a finite group G, then the character hypergroup of G modulo that of G/K is isomorphic to the hypergroup of G-conjugacy classes of the irreducible characters of K.

Bibliography

  1. [1]

    C. W. Curtis -I. Reiner,Representation Theory of Finite Groups and Associative Algebras, Interscience, New York, 1962.

  2. [2]

    A. P. Dietzman,On the multigroups of complete conjugate sets of elements of a group, C. R. (Doklady) Acad. Sci. URSS (N.S.),49 (1946), pp. 315–317.

  3. [3]

    A. P. Dietzman,On multigroups whose elements are subsets of a group (Russian), Moskov Gos. Ped. Inst. Uc. Zap.,71 (1953, pp. 71–79. (Math. Rev.,17 (1956), p. 826).

  4. [4]

    M. Drescher -O. Ore,Theory of Multigroups, Amer. J. Math.,60 (1938), pp. 705–733.

  5. [5]

    W. Feit,Characters of Finite Groups, Benjamin, New York, 1967.

  6. [6]

    E. Formanek,The conjugation representation and fusionless extensions, Proc. Amer. Math. Soc.,30 (1971), pp. 73–75.

  7. [7]

    J. S. Frame,On the conjugating representation, Bull. Amer. Math. Soc.,53 (1948), pp. 584–580.

  8. [8]

    J. S. Frame, Review of [14], Math. Reviews,44 (1972), p. 1246, no. 6860.

  9. [9]

    M. Hall Jr.,The Theory of Groups, Macmillan, New York, 1959.

  10. [10]

    S. Helgason,Lacunary Fourier Series on non-commutative groups, Proc. Amer. Math. Soc.,9 (1958), pp. 782–790.

  11. [11]

    E. Hewitt -K. Ross,Abstract Harmonic Analysis, II, Springer, Berlin, 1971.

  12. [12]

    R. Iltis,Some algebraic structures in the dual of a compact Group, Can. Jr. Math.,20 (1968), pp. 1499–1510.

  13. [13]

    N. Iwahori -H. Matsumoto,Several remarks on projective representation of finite groups. Jr. Fac. Sci. Univ. Tokyo, section 2, Math. Astro. Phys. Chem.,10 (1964), pp. 129–146.

  14. [14]

    R. L. Roth,On the conjugating representation of a finite group, Pac. Jr. Math.,36 (1971), pp. 515–521.

  15. [15]

    R. L. Roth,A dual view of the Clifford theory of characters of finite groups, Can. Jr. Math.,23 (1971), pp. 857–865.

Download references

Author information

Additional information

Entrata in Redazione l’8 gennaio 1974.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Roth, R.L. Character and conjugacy class hypergroups of a finite group. Annali di Matematica 105, 295–311 (1975). https://doi.org/10.1007/BF02414935

Download citation

Keywords

  • Normal Subgroup
  • Finite Group
  • Conjugacy Class
  • Irreducible Character