# Semantic search

Abelian normal is not join-closed, Abelian normal not implies central, Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith, Abelian-quotient abelian normal subgroup is contained in centralizer of derived subgroup, Abelian-to-normal replacement theorem for prime exponent, Any abelian normal subgroup normalizes an abelian subgroup of maximum order, Automorphism group action lemma for quotients, Central implies abelian normal, Degree of irreducible projective representation divides index of abelian normal subgroup to which its cohomology class restricts trivially, Degree of irreducible representation divides index of abelian normal subgroup, Elementary abelian-to-normal replacement theorem for large primes, Every finite group has an abelian normal subgroup whose order is divisible by the orders of all abelian normal subgroups, Existence of abelian normal subgroups of small prime power order, Group of prime-sixth or higher order contains abelian normal subgroup of prime-fourth order for prime equal to two, Jordan-Schur theorem on abelian normal subgroups of small index, P-constrained and p-stable implies abelian normal subgroup of Sylow subgroup is contained in (p',p)-core, Quotient-pullbackable implies linearly pushforwardable for representation over prime field, Series-equivalent abelian-quotient abelian not implies automorphic