A BOUND ON THE p-LENGTH OF P-SOLVABLE GROUPS. (January 2015)

• Record Type: Journal Article
• Authors: GONZÁLEZ-SÁNCHEZ, JON; SPAGNUOLO, FRANCESCA
• Is Part Of: Glasgow mathematical journal. Volume 57:Part 1(2015:Jan.)
• Page Start: 167
• Page End: 171
• Publication Date: 2015-01
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089514000196
• Languages: English
• ISSNs: 0017-0895

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>Let <italic>G</italic> be a finite <italic>p</italic>-solvable group and <italic>P</italic> a Sylow <italic>p</italic>-subgroup of <italic>G</italic>. Suppose that <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj46nhn3k" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\gamma_{\ell (p-1)}(P)\subseteq \gamma_r(P)^{p^s}$]]></tex-math></alternatives></inline-formula> for ℓ(<italic>p</italic>−1) &lt; <italic>r</italic> + <italic>s</italic>(<italic>p</italic> − 1), then the <italic>p</italic>-length is bounded by a function depending on ℓ.</p> </abstract>