Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

SOME SUPERSOLVABILITY CONDITIONS FOR FINITE GROUPS

F. Barry, D. MachHale and À. Ní Shé
Mathematical Proceedings of the Royal Irish Academy
Vol. 106A, No. 2 (December 2006), pp. 163-177
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/40656943
Page Count: 15
  • Read Online (Free)
  • Download ($10.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
SOME SUPERSOLVABILITY CONDITIONS FOR FINITE GROUPS
Preview not available

Abstract

To investigate the intuitive notion that the closer a group is to being abelian the more likely it is to be supersolvable, we investigate situations where the following indicators of commutativity are ' large'— the reciprocal of the index |G'|; reciprocal of |G'|; $Pr(G)\, = \,{{K(G)} \over {|G|}}$; $f(G)\, = \,\sum\nolimits_{i = 1}^k {{{di} \over {|G|}}} $ and l(G), the maximum proportion of elements inverted by an automorphism. Applications to groups that satisfy the converse of Lagrange's Theorem are deduced.

Page Thumbnails

  • Thumbnail: Page 
[163]
    [163]
  • Thumbnail: Page 
164
    164
  • Thumbnail: Page 
165
    165
  • Thumbnail: Page 
166
    166
  • Thumbnail: Page 
167
    167
  • Thumbnail: Page 
168
    168
  • Thumbnail: Page 
169
    169
  • Thumbnail: Page 
170
    170
  • Thumbnail: Page 
171
    171
  • Thumbnail: Page 
172
    172
  • Thumbnail: Page 
173
    173
  • Thumbnail: Page 
174
    174
  • Thumbnail: Page 
175
    175
  • Thumbnail: Page 
176
    176
  • Thumbnail: Page 
177
    177