Counting Nilpotent Pairs in Finite Groups

Jason E. Fulman; Michael D. Galloy; Gary J. Sherman; Jeffrey M. Vanderkam

Counting Nilpotent Pairs in Finite Groups

Jason E. Fulman
, Michael D. Galloy
, Gary J. Sherman
, Jeffrey M. Vanderkam

Mauna Loa Solar Observatory

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let G be a finite group and let v_i(G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the v_i's are established. In particular it is shown that v_i = k_i·|G|/|G|² for some non-negative integer k_i and that Σ^∞_i=1i v_i is either 1 or at most 1/2 for solvable groups.

Original language	English
Pages (from-to)	161-178
Number of pages	18
Journal	Ars Combinatoria
Volume	54
State	Published - Jan 2000

Cite this

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title = "Counting Nilpotent Pairs in Finite Groups",

abstract = "Let G be a finite group and let vi(G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the vi's are established. In particular it is shown that vi = ki·|G|/|G|2 for some non-negative integer ki and that Σ∞i=1i vi is either 1 or at most 1/2 for solvable groups.",

author = "Fulman, \{Jason E.\} and Galloy, \{Michael D.\} and Sherman, \{Gary J.\} and Vanderkam, \{Jeffrey M.\}",

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T1 - Counting Nilpotent Pairs in Finite Groups

AU - Fulman, Jason E.

AU - Galloy, Michael D.

AU - Sherman, Gary J.

AU - Vanderkam, Jeffrey M.

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N2 - Let G be a finite group and let vi(G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the vi's are established. In particular it is shown that vi = ki·|G|/|G|2 for some non-negative integer ki and that Σ∞i=1i vi is either 1 or at most 1/2 for solvable groups.

AB - Let G be a finite group and let vi(G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the vi's are established. In particular it is shown that vi = ki·|G|/|G|2 for some non-negative integer ki and that Σ∞i=1i vi is either 1 or at most 1/2 for solvable groups.

UR - https://www.scopus.com/pages/publications/0346342150

M3 - Article

AN - SCOPUS:0346342150

SN - 0381-7032

VL - 54

SP - 161

EP - 178

JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

Counting Nilpotent Pairs in Finite Groups

Abstract

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