Geodesic
On regularity of Sylow $p$-subgroups of the Chevalley group of types $F_4, E_6$ over the ring $\mathbb{Z}_{p^m}$
The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 101-115

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In this paper, we find necessary and sufficient conditions for the regularity of the Sylow $p$-subgroup $P$ of the Chevalley group of types $F_4$ or $E_6$ defined over the ring of integers modulo $p^m$ when $p$ is a prime different from $37,41,43,47$. For the listed values of $p,$ the group $P$ is regular if the exponent $m$ does not exceed $3$; for $m$ greater than $3$, the answer remains unknown.
Keywords: regular $p$-group, Sylow subgroup, Chevalley group. 
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     author = {S. G. Kolesnikov and A. I. Polovinkina},
     title = {On regularity of {Sylow} $p$-subgroups of the {Chevalley} group of types $F_4, E_6$ over the ring $\mathbb{Z}_{p^m}$},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {101--115},
     publisher = {mathdoc},
     volume = {51},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a6/}
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S. G. Kolesnikov; A. I. Polovinkina. On regularity of Sylow $p$-subgroups of the Chevalley group of types $F_4, E_6$ over the ring $\mathbb{Z}_{p^m}$. The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 101-115. http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a6/