Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

SIMPLICITY OF GROUPS OF EVEN ORDER

  • Choi, Minjung (Department of Mathematics Sookmyung Women's University) ;
  • Park, Seungkook (Department of Mathematics Sookmyung Women's University)
  • Received : 2014.04.22
  • Accepted : 2014.07.10
  • Published : 2014.08.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{\geq}3$, are not simple and groups of order $2^npq^t$ for $t{\geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.

Keywords

References

  1. W. Burnside, On Groups of Order $p^{\alpha}q^{\beta}$, Proc. London Math. Soc. S2-1 (1904), no. 1, 388-392. https://doi.org/10.1112/plms/s2-1.1.388
  2. W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), no. 3, 775-1029. https://doi.org/10.2140/pjm.1963.13.775
  3. J. N. Salunke and A. R. Gotmare, Converse of Lagrange's theorem and solvable groups, Bull. Marathwada Math. Soc. 10 (2009), no. 1, 36-42.