Synthesis of thyroliberin

A two-stage method for the synthesis of thyroliberin is proposed. A complex of the sodium salt of histidine with 15-crown-5 is used for the protection of the carboxylic fraction of histidine.A. V. Bogatskii Physicochemical Institute, Academy of Sciences of the Ukrainian SSR, Odessa. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 222–224, March–April, 1986.     

On finite groups isospectral to simple symplectic and orthogonal groups

The spectrum of a finite group is the set of its element orders. Two groups are said to be isospectral if their spectra coincide. We deal with the class of finite groups isospectral to simple and orthogonal groups over a field of an arbitrary positive characteristic p. It is known that a group of this class has a unique nonabelian composition factor. We prove that this factor cannot be isomorphic to an alternating or sporadic group. We also consider the case where this factor is isomorphic to a group of Lie type over a field of the same characteristic p.     

On local finiteness of some groups of period 12

The local finiteness is proven of all groups of period 12 in which the order of the product of every two involutions is at most 4.     

Infinite Groups Containing a Proper Hughes Subgroup H3(G)

Algebra and Logic - We consider groups in which H3(G) is both nontrivial and proper. In particular, it is proved that in such a group, |G : H3(G)| = 3.     

A characterization of alternating groups. II

Let G be a group. A subset X of G is called an A-subset if X consists of elements of order 3, X is invariant in G, and every two non-commuting members of X generate a subgroup isomorphic to A₄ or to A₅. Let X be the A-subset of G. Define a non-oriented graph Γ(X) with vertex set X in which two vertices are adjacent iff they generate a subgroup isomorphic to A₄. Theorem 1 states the following. Let X be a non-empty A-subset of G. (1) Suppose that C is a connected component of Γ(X) and H = 〈C〉. If H ∩ X does not contain a pair of elements generating a subgroup isomorphic to A₅ then H contains a normal elementary Abelian 2-subgroup of index 3 and a subgroup of order 3 which coincides with its centralizer in H. In the opposite case, H is isomorphic to the alternating group A(I) for some (possibly infinite) set I, |I| ≥ 5. (2) The subgroup 〈X^G〉 is a direct product of subgroups 〈C _α〉-generated by some connected components C _α of Γ(X). Theorem 2 asserts the following. Let G be a group and X⊆G be a non-empty G-invariant set of elements of order 5 such that every two non-commuting members of X generate a subgroup isomorphic to A₅. Then 〈XG〉 is a direct product of groups each of which either is isomorphic to A₅ or is cyclic of order 5. Supported by RFBR grant No. 05-01-00797; FP “Universities of Russia,” grant No. UR.04.01.028; RF Ministry of Education Developmental Program for Scientific Potential of the Higher School of Learning, project No. 511; Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1. __________ Translated from Algebra i Logika, Vol. 45, No. 2, pp. 203–214, March–April, 2006.     

Finite groups with 2-Sylow intersections of rank≤2

We describe finite simple groups in which each elementary subgroup of order 8 lies in no more than one Sylow 2-subgroup.     

Finite simple groups whose Sylow 2-subgroups possess an extra-special subgroup of index 2

Let G be a finite simple group with Sylow 2-subgroup T. If there is an extra-special sub-group of index 2 in T, then G is isomorphic to one of the following groups: $$\mathop {M_{11,} }\limits_{U_3 (q),}$$ for an appropriate odd q.