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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-03-28 and was most recently seen on 2026-03-28.
In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever g is not in H.
The Bender–Suzuki theorem, proved by Bender (1971) extending work of Suzuki (1962, 1964), classifies the groups G with a strongly embedded subgroup H. It states that eitherG has cyclic or generalized quaternion Sylow 2-subgroups and H contains the centralizer of an involution
or G/O(G) has a normal subgroup of odd index isomorphic to one of the simple groups PSL2(q), Sz(q) or PSU3(q) where q≥4 is a power of 2 and H is O(G)NG(S) for some Sylow 2-subgroup S.
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