On $\pi ’$-closure of $\pi$-homogeneous groups
HTML articles powered by AMS MathViewer
- by Pamela Ferguson
- Proc. Amer. Math. Soc. 66 (1977), 9-12
- DOI: https://doi.org/10.1090/S0002-9939-1977-0450397-9
- PDF | Request permission
Abstract:
Let $\pi$ be a set of odd primes. It is known that $\pi ’$-closed groups are $\pi$-homogeneous, but that the converse does not hold in general. In this paper we prove that a finite group G which is ${D_\pi }$ and $\pi$-homogeneous is $\pi ’$-closed.References
- Zvi Arad, $\pi$-homogeneity and $\pi ^{\prime }$-closure of finite groups, Pacific J. Math. 51 (1974), 1–9. MR 346048, DOI 10.2140/pjm.1974.51.1
- Reinhold Baer, Closure and dispersion of finite groups, Illinois J. Math. 2 (1958), 619–640. MR 104732
- W. Feit, On a conjecture of Frobenius, Proc. Amer. Math. Soc. 7 (1956), 177–187. MR 77532, DOI 10.1090/S0002-9939-1956-0077532-5
- Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- I. Martin Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460423
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 9-12
- MSC: Primary 20D20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0450397-9
- MathSciNet review: 0450397