In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

Let $G$ be a reductive group over an algebraically closed field $k$ of separably good characteristic $p>0$ for . Under these assumptions, Springer isomorphism $\phi : \mathcal {N}_{\mathrm {red}}(\mathfrak {g}) \rightarrow {V}_{\mathrm {red}}(G)$ from the nilpotent scheme $\mathfrak {g}$ to unipotent always exists and allows one integrate any $p$ -nilpotent element into One should wonder whe...

This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups. A similar proof was given later by A. Borel and J. Tits (see also bibliographical remarks in the introduction to their paper). I.I. Pyatetskii–Shapiro suggested me to prove the following theorem which in his opinion would be of interest for the theory of discre...

The spectral sequence associated to the Arone-Goodwillie tower for the n-fold loop space functor is used to show that the first two non-trivial layers of the nilpotent filtration of the reduced mod 2 cohomology of a (sufficiently connected) space with nilpotent cohomology are comparable. This relies upon the theory of unstable modules over the mod 2 Steenrod algebra, together with properties of...

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

BACKGROUND Our previous studies have demonstrated that the levels of 5-hydroxytryptamine (5-HT) and 5-HT 2A receptor (5-HT2AR) in serum and platelet were associated with depression and myocardial infarction (MI), and pretreatment with ginseng fruit saponins (GFS) before MI and depression had an effect on the 5-HT system. In this study, the effects of GFS on the 5-HT system in the Sprague-Dawley...

An automorphism of a group G is called regular if it moves every element of G except the identity. BURNSIDE proved that a finite group G has a regular automorphism of order two if and only if G is an abelian group of odd order, and then the only such automorphism maps every element onto its inverse ([21, p. 230). More recently several authors considered the question: what groups can admit regul...

We prove that the Duflo-Serganova functor DSx attached to an odd nilpotent element x of osp(m|2n) is semisimple, i.e. sends a semisimple representation M osp(m−2k|2n−2k) where k rank x. closed formula for DSx(L(λ)) in terms arc diagram λ.

Introduction: Impaired wound healing in diabetic patients is a major clinical problem, which is associated with significant morbidity and mortality. Estrogen has positive effects on neoangiogenesis, reepithelialization and cell proliferation. In this research, effect of estrogen on wound healing in diabetic male rats was investigated. Methods: This study was performed on male Wistar rats (bo...

Let G be a reductive algebraic group, with nilpotent cone N and flag variety B. We construct an exact functor from perverse sheaves on N to locally constant sheaves on B, and we use it to study Ext-groups and stalks of simple perverse sheaves on N in terms of the cohomology of B. 2010 Mathematics Subject Classification: Primary 20G05; Secondary 14F05, 32S60.