Geodesic
On finite groups isospectral to $PSp_4(q)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 64-69

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The spectrum of a finite group is the set of its element orders. Let $q$ be a power of a prime $p$, with $p \geqslant 5$. It is known that any finite group having the same spectrum as the simple symplectic group $PSp_4(q)$ either is isomorphic to an almost simple group with socle $PSp_4(q)$ or can be homomorphically mapped onto an almost simple group $H$ with socle $PSL_2(q^2)$. We prove that the group $H$ cannot coincide with $PSL_2(q^2)$, i.e., $H$ must contain outer automorphisms of its socle.
Keywords: finite group, element order. 
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     title = {On finite groups isospectral to $PSp_4(q)$},
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M. A. Grechkoseeva; V. M. Rodionov. On finite groups isospectral to $PSp_4(q)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 64-69. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a5/