# Semantic search

Analogue of focal subgroup theorem for Hall subgroups, Hall and hyperfocal implies retract, Hall does not satisfy transfer condition, Hall implies join of Sylow subgroups, Hall implies order-conjugate in solvable, Hall implies order-dominating in finite solvable, Hall implies paracharacteristic, Hall is transitive, Hall not implies WNSCDIN, Hall not implies automorph-conjugate, Hall not implies order-conjugate, Hall not implies order-isomorphic, Hall not implies procharacteristic, Hall not implies pronormal, Hall satisfies intermediate subgroup condition, Hall satisfies permuting transfer condition, Hall subgroups exist in finite solvable group, Hall subgroups need not exist, Nilpotent Hall implies isomorph-conjugate, Nonsolvable proper Hall subgroup of symmetric group is contained in symmetric group on subset of size one less