Abstract Given a finite group G , we denote by $L(G)$ the subgroup lattice of and ${\cal CD}(G)$ Chermak–Delgado . In this note, determine groups such that $|{\cal CD}(G)|=|L(G)|-k$ for $k=1,2$

Notation and Terminology. Given a finite lattice L, the expression L ∼= [H,G] means “there exist finite groups H < G such that L is isomorphic to the interval {K | H 6 K 6 G} in the subgroup lattice of G.” A group G is called almost simple if G has a normal subgroup S P G which is nonabelian, simple, and has trivial centralizer, CG(S) = (e). If H 6 G, then the core of H in G, denoted coreG(H), ...

Let l be an oriented link of d components with nonzero Alexander polynomial ∆(u1, . . . , ud). Let Λ be a finite-index subgroup of H1(S− l) ∼= Z, and let MΛ be the corresponding abelian cover of S branched along l. The growth rate of the order of the torsion subgroup of H1(MΛ), as a suitable measure of Λ approaches infinity, is equal to the Mahler measure of ∆.

AIM To evaluate the therapeutic effects of ursodeoxycholic acid (UDCA) on autoimmune hepatitis (AIH). METHODS A total 136 patients who were diagnosed with AIH were included in our study. All of the patients underwent a liver biopsy, and had at least a probable diagnosis on the basis of either the revised scoring system or the simplified scores. Initial treatment included UDCA monotherapy (Gro...

We give a necessary and sufficient condition for pair of parabolic subgroups $P$ $Q$ $G=GL_n(\mathbb{R})$ such that the tensor product any two unitarily induced representations from are tempered. also an $L^p$-estimate matrix coefficients regular on $L^2(G/L)$ when $L$ is Levi subgroup $G$.

OBJECTIVE Increased QT interval dispersion (QTd) is an electrocardiographic parameter shown to be associated with malignant ventricular arrhythmias and sudden death, and QT dispersion corrected for heart rate (QTc) has emerged as a potentially important predictor of cardiac death. Increased QTd has been detected to be directly related to thyroid-stimulating hormone (TSH) levels in overt hypothy...

Let L be a simply-connected simple connected algebraic group over number field F, and H semisimple absolutely maximal F-subgroup of L. $$\Delta (H)$$ the image diagonally embedded in $$L^n$$ . Under cohomological condition, we prove an asymptotic formula for rational points bounded height on projective equivariant compactifications (H)\backslash L^n$$ with respect to balanced line bundle.

Note that the intersection property in Theorem A is equivalent to saying that NL(P ) is a p-group. Also, since this property is clearly independent of the choice of P in Sylp(G), it is clear that L is characteristic in G. Our interest in this characteristic subgroup was motivated by the following. Theorem B. Suppose that G is p-solvable and let L be the largest normal subgroup of G such that L∩...

OBJECTIVE To investigate the prevalence of subclinical hypothyroidism (SH) diagnosed by thyrotropin-releasing hormone (TRH) stimulating test in infertile women with basal thyroid-stimulating hormone (TSH) levels of 2.5 to 5.0 mIU/L. METHODS This study was performed in 39 infertile women with ovulatory disorders (group 1) and 27 infertile women with male infertility only (group 2, controls) wh...

Let $$p \geqslant 3$$ be a prime integer and, for $$l 1$$ , let $$G \cong {{\mathbb {Z}}}_{p}^{l}$$ group of conformal automorphisms some closed Riemann surface S genus $$g 2$$ . By the Riemann–Hurwitz formula, either \leqslant g+1$$ or $$p=2\,g+1$$ If $$l=1$$ and then S/G is sphere with exactly three cone points if moreover 11$$ G unique p-Sylow subgroup $$\textrm{Aut}\hspace{0.55542pt}(S)$$ $...