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@article{Guralnick:2019:10.1007/s11856-018-1794-x,
author = {Guralnick, R and Liebeck, MW},
doi = {10.1007/s11856-018-1794-x},
journal = {Israel Journal of Mathematics},
pages = {181--191},
title = {Permutation representations of nonsplit extensions involving  alternating groups},
url = {http://dx.doi.org/10.1007/s11856-018-1794-x},
volume = {229},
year = {2019}
}

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TY  - JOUR
AB  - L. Babai has shown that a faithful permutation representation of a nonsplit extension of a group by an alternating group Ak must have degree at least k2(12−o(1)), and has asked how sharp this lower bound is. We prove that Babai’s bound is sharp (up to a constant factor), by showing that there are such nonsplit extensions that have faithful permutation representations of degree 32k(k−1). We also reprove Babai’s quadratic lower bound with the constant 1/2 improved to 1 (by completely different methods).
AU  - Guralnick,R
AU  - Liebeck,MW
DO  - 10.1007/s11856-018-1794-x
EP  - 191
PY  - 2019///
SN  - 0021-2172
SP  - 181
TI  - Permutation representations of nonsplit extensions involving  alternating groups
T2  - Israel Journal of Mathematics
UR  - http://dx.doi.org/10.1007/s11856-018-1794-x
UR  - http://hdl.handle.net/10044/1/58417
VL  - 229
ER  -

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