Journal of Group Theory
Editor-in-Chief: Parker, Christopher W.
Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus
IMPACT FACTOR 2018: 0.470
5-year IMPACT FACTOR: 0.520
CiteScore 2018: 0.53
SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047
Mathematical Citation Quotient (MCQ) 2018: 0.48
In 1878, Jordan showed that a finite subgroup of GL(n, ℂ) must possess an abelian normal subgroup whose index is bounded by a function of n alone. We will give the optimal bound for all n; for n ⩾ 71, it is (n + 1)!, afforded by the symmetric group S n+1. We prove a ‘replacement theorem’ that enables us to study linear groups by breaking them down into individual primitive constituents and we give detailed information about the structure of the groups that achieve the optimal bounds, for every degree n.
Our proof relies on known lower bounds for the degrees of faithful representations of each quasisimple group, depending on the classification of finite simple groups, through the use of the bounds for primitive groups that the author has previously obtained.
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