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$(2B, 3A, 5A)$-subalgebras of the Griess algebra with alternating Miyamoto group
We use Majorana representations to study the subalgebras of the Griess algebra that have shape $(2B,3A,5A)$ and whose associated Miyamoto groups are isomorphic to $A_n$. We prove that these subalgebras exist only if $n\in \{5,6,8\}$. The case $n=5$ was already treated by Ivanov, Seress, McInroy, and
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