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During the Chinese New Year of 2007, I received a long distance call from the United Kingdom. The president of the Chartered Institute of Building (CIOB), Professor Roger Flanagan, was [...]

This paper classifies the finite groups in which any nonmaximal abelian subgroups do not have any nontrivial inner automorphisms.

Let Gbe a finite group and let Mbe a maximal subgroup of G. Let K/Lbe a chief factor of Gsuch that L≤Mand G=MK. We call the group M∪K/La c-section of Min G. All c-sections of Mare isomorphic. Using the concept of c-sections, we obtain some new characterizations of solvable and π-solvable groups.

A modified surgical method for penis lengthening was, for the first time, set up in this laboratory. The procedure involves covering the dissected corpus cavernosum with either a scrotal flap or a skin graft after releasing the superficial ligament and even some deep suspensory ligament. The advantage of the scrotal flap is emphasized to cover the wound, and a V−Y suture was made to avoid the traction. The results, both in appearance and increased length, were satisfactory in 52 cases. Among the 52 patients, 39 suffered from congenital short penis and 13 from traumatic injuries. The significance and the blood supply of the penis are discussed.

When a contract dispute arises, the parties concerned should try to reach a settlement through negotiation as soon as possible. If negotiation fails, either party may apply for mediation or arbitration through the agency designated by the state for contract management or file a lawsuit directly with the People's Court.

Let Mbe a maximal subgroup of a finite group G. A pair of subgroups (C, D) of Gis called a θ-pair of Mif it satisfies the following conditions: (a) D≤ Cand D⊲ G; (b) (M,C) = Gand D≤ M;(c) C/Dhas no proper normal subgroup of G/D. A θ-pair (C,D) of Mis said to be maximal if Mhas no θ-pair (C',D') such that C < C'. In this paper we obtain several results on maximal θ-pairs which imply Gto be solvable or supersolvable.

In this paper, the minimal subgroups of a finite group G are studied. Using the normalizes of Sylow subgroups of G, we obtain some sufficient conditions for G to be p-milpotent and supersolvable, which ae extensions of the related results of Burnside, Ito, Buckley and Asaad.

Abstract: LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions: