Abstract
AbstractMajorana theory is an axiomatic tool for studying the Monster group M and its subgroups through the 196,884-dimensional Conway–Griess–Norton algebra. The theory was introduced by A. A. Ivanov in 2009 and since then it experienced a remarkable development including the classification of Majorana representations for small (and not so small) groups. The group $$U_3(5)$$
U
3
(
5
)
is (isomorphic to) the socle of the centralizer in M of a subgroup of order 25. The involutions of this $$U_3(5)$$
U
3
(
5
)
-subgroup are 2A-involutions in the Monster. Therefore, $$U_3(5)$$
U
3
(
5
)
possesses a Majorana representation (based on the embedding in the Monster). We prove that this is the unique Majorana representation of $$U_3(5)$$
U
3
(
5
)
, calculate its dimension, which is 798, and obtain a description in terms of the Hoffman–Singleton graph of which the automorphism group has $$U_3(5)$$
U
3
(
5
)
as an index 2 subgroup.
Publisher
Springer Science and Business Media LLC
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