Geodesic
On Ditsman's lemma
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 150-157

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Let $H$ be a subgroup of a group $G$ generated by a finite $G$-invariant subset $X=\bigcup_{i=1}^kC_i$ that consists of elements of finite order, where $C_i$ is the class of conjugate elements of $G$ with representative $a_i$. We prove that $$ |H|\leq\prod_{i=1}^ko(a_i)^{|C_i|}, $$ where $o(a_i)$ is the order of the element $a_i\in C_i$. Best estimates are obtained for some important special cases.
Mots-clés : simple group, Lie type group, sporadic simple group, quasisimple group. 
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     author = {L. S. Kazarin},
     title = {On {Ditsman's} lemma},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {150--157},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a14/}
}
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L. S. Kazarin. On Ditsman's lemma. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 150-157. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a14/