Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the solvability of groups of central type


Author: Jay Yellen
Journal: Proc. Amer. Math. Soc. 52 (1975), 50-54
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9939-1975-0374261-7
MathSciNet review: 0374261
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a finite group with center $ Z$8 and irreducible complex character $ x$ so that $ x{(1)^2} = [G:Z]$, If the $ 2$-Sylow subgroup of $ G/Z$ has order 16 or less then $ G$ is solvable.


References [Enhancements On Off] (What's this?)

  • [1] G. D. Birkhoff and H. S. Vandiver, "On the integral divisors of $ {a^n} - {b^n}$,'' in George David Birkhoff: Collected mathematical papers. Vol. 3, Amer. Math. Soc., Providence, R. I., 1950, pp. 145-152.
  • [2] F. R. DeMeyer, Groups with an irreducible character of large degree are solvable, Proc. Amer. Math. Soc. 25 (1970), 615-617. MR 43 #368. MR 0274605 (43:368)
  • [3] -, Irreducible characters and solvability of finite groups, Pacific J. Math. 41 (1972), 347-353. MR 48 #402. MR 0322038 (48:402)
  • [4] F. R. DeMeyer and G. J. Janusz, Finite groups with an irreducible representation of large degree, Math. Z. 108 (1969), 145-153. MR 38 #5910. MR 0237629 (38:5910)
  • [5] W. Feit, The current situation on the theory of finite simple groups, Proc. Internat. Congress Math. (Nice, 1970), vol. 1, Gauthier-Villars, Paris, 1971, pp. 55-93. MR 0427449 (55:481)
  • [6] S. M. Gagola, Characters fully ramified over a normal subgroup, University of Wisconsin (preprint).
  • [7] D. Gorenstein, Finite groups, Harper & Row, New York, 1968. MR 38 #229. MR 0231903 (38:229)
  • [8] H. Matsumoto and N. Iwahori, Several remarks on projective representations of finite groups, J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 129-146. MR 31 #4841. MR 0180607 (31:4841)
  • [9] H. Pahlings, Gruppen mit irreduziblen Darstellungen hohen Grades, Mitt. Math. Sem. Giessen 85 (1970), 27-44. MR 41 #8537. MR 0263938 (41:8537)
  • [10] R. Ree, A family of simple groups associated with the simple Lie algebra of type $ ({G_2})$, Amer. J. Math. 83 (1961), 432-462. MR 25 #2123. MR 0138680 (25:2123)
  • [11] W. R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 29 #4785. MR 0167513 (29:4785)
  • [12] K. Timmer, Subgroups of groups of central type, Trans. Amer. Math. Soc. 189 (1974), 133-161. MR 0357574 (50:10042)
  • [13] H. N. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62-89. MR 33 #5752. MR 0197587 (33:5752)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D10

Retrieve articles in all journals with MSC: 20D10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374261-7
Keywords: Finite group, irreducible complex character, solvable group, simple group
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society