Premium
Probabilistic generation of finite groups with a unique minimal normal subgroups
Author(s) -
Detomi E.,
Lucchini A.
Publication year - 2013
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jds076
Subject(s) - profinite group , modulo , mathematics , probabilistic logic , normal subgroup , group (periodic table) , combinatorics , discrete mathematics , pure mathematics , physics , statistics , quantum mechanics
Let L be a finite group with a unique minimal normal subgroup, say N . We study the conditional probability P L, N ( d ) that d randomly chosen elements of L generate, L given that they generate L modulo N . In particular, we prove that if d ⩾ d ( L ), then P L, N ( d )⩾½. Several applications to general questions on the generation of finite and profinite groups are described.