The Existence of Minimal Logarithmic Signatures for some Finite Simple Unitary Groups

2019/08/12 by Rahimipour, A. R., Ashrafi, A. R.
#$20D08$ #$94A60$ #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1908.04125

Abstract

The MLS conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups PSU_n(q). We report a gap in the proof of the main result of [H. Hong, L. Wang, Y. Yang, Minimal logarithmic signatures for the unitary group U_n(q), Des. Codes Cryptogr. 77 (1) (2015) 179--191] and present a new proof in some special cases of this result. As a consequence, the MLS conjecture is still open.

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