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- W4297407629 abstract "For an element $g$ in a group $X$, we say that $g$ has 2-part order $2^{a}$ if $2^{a}$ is the largest power of 2 dividing the order of $g$. We prove lower bounds on the proportion of elements in finite classical groups in odd characteristic that have certain 2-part orders. In particular, we show that the proportion of odd order elements in the symplectic and orthogonal groups is at least $C/ell^{3/4}$, where $ell$ is the Lie rank, and $C$ is an explicit constant. We also prove positive constant lower bounds for the proportion of elements of certain 2-part orders independent of the Lie rank. Furthermore, we describe how these results can be used to analyze part of Yalc{c}inkaya's Black Box recognition algorithm for finite classical groups in odd characteristic." @default.
- W4297407629 created "2022-09-28" @default.
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- W4297407629 date "2010-07-18" @default.
- W4297407629 modified "2023-09-23" @default.
- W4297407629 title "Proportions of elements with given 2-part order in finite classical groups of odd characteristic" @default.
- W4297407629 doi "https://doi.org/10.48550/arxiv.1007.2983" @default.
- W4297407629 hasPublicationYear "2010" @default.
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