Nilpotent subgroups of finite soluble groups

On locally finite groups whose cyclic subgroups are monopronormal

“…Recall that a subgroup H of a group G is said to be abnormal in G if for each element g ∈ G we have g ∈ H, H g . Recall also that a subgroup H of a group G is contranormal in G if H G = G. Note that every abnormal subgroup is contranormal (see, for example, [1]).…”

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

“…Following J. Rose [21], we call a subgroup H of a group G contranormal in G if H G = G. L. A. Kurdachenko and H. Smith [10] described the groups in which all subgroups are either subnormal or selfnormalizing.…”

Maximal Nilpotent Subgroups of Finite Soluble Groups

“…In Proposition 1.8 of [6], Rose gave a number of conditions on a Max^-subgroup M of a 9i 2 -group G equivalent to M being pronormal in G. We note that this is equivalent to a very natural condition on the associated standard subgroup. This result means that ty k n 9t 2 is the class of 9Z 2 -groups in which there are at most k standard subgroups and these are all normal in G.…”

“…the natural split extension of F by K, where F = Dr <x,> is elementary Abelian of order 26 . ' = 1 K has two conjugacy classes of Maxjj-subgroups: FittK=(a,b 2 ) and Cart(K) = {(b}} K .…”