86,706 research outputs found

    A group of generalized finitary automorphisms of an abelian group

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    We study the group IAut(A) generated by the inertial automorphisms of an abelian group A, that is, automorphisms f with the property that each subgroup H of A has finite index in the subgroup generated by H and f(H) . Clearly, IAut(A) contains the group FAut(A) of finitary automorphisms of A, which is known to be locally finite. In a previous paper, we showed that IAut(A) is (locally finite)-by-abelian. In this paper, we show that IAut(A) is also metabelian-by-(locally finite). More precisely, IAut(A) has a normal subgroup N such that IAut(A) /N is locally finite and the derived subgroup of N 0 is an abelian periodic subgroup all of whose subgroups are normal in N. In the case when A is periodic, IAut(A) turns out to be abelian-by-(locally finite) indeed, while in the general case it is not even (locally nilpotent)-by-(locally finite). Moreover, we provide further details about the structure of IAut(A)

    GROUPS WITH THE REAL CHAIN CONDITION ON NON-PRONORMAL SUBGROUPS

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    It is shown that a generalised radical group has no chain of non-pronormal subgroups with the same order type as the set R of the real numbers if and only if either the group is minimax or all subgroups are pronormal

    Groups in which each subnormal subgroup is commensurable with some normal subgroup

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    We study groups in which each subnormal subgroup is commensurable with a normal subgroup. Recall that two subgroups and are termed commensurable if H-KHcap K has finite index in both and . Among other results, we show that if a (sub)soluble group has the above property, then is finite-by-metabelian, i.e., GG{} is finite

    On groups with all proper subgroups finite-by-abelian-by-finite

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    We show that if all proper subgroups of a locally graded group G are finite-by-abelian-by-finite, then G contains a finite normal subgroup N such that all proper subgroups of G/N are abelian-by-finite. Then we apply this result to the study of groups which are minimal-non-P also for related group properties P. Finally we see how for locally (soluble-by-finite) groups of infinite rank, it is enough to restrict attention to the proper subgroups with infinite rank

    The weak minimal condition on subgroups which fail to be close to normal subgroups

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    A subgroup H of a group G is commensurable (or close) to a normal subgroup if there is a normal subgroup N of G such that the index |HN:(H∩N)| is finite; if further the subgroup N can be chosen to be contained in H, i.e. if H/HG is finite, then H is called core-finite. We describe the structure of (generalized) soluble groups satisfying the weak minimal condition on subgroups that are not commensurable with a normal subgroup. Our results describe also (generalized) soluble groups satisfying the weak minimal condition on non-(core-finite) subgroups

    Non-thyroidal illness syndrome and short-term survival in a hospitalised older population

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    BACKGROUND: non-thyroidal illness syndrome (NTIS) has been associated with an adverse clinical outcome. OBJECTIVE: to evaluate the prevalence of NTIS, its impact on patients' survival and the possible pathogenic role of systemic inflammation. DESIGN:observational cross-sectional analysis. PARTICIPANTS AND SETTING:three hundred and one acutely ill older patients (156 women; median age 81 years, range 65-101) consecutively admitted to a primary care unit. METHODS: serum FT(3), FT(4) and thyrotropin levels as well as acute inflammation indexes were evaluated. RESULTS: the NTIS prevalence (specifically low T3 syndrome) was 31.9%. A significant association was found between NTIS and acute renal failure (P = 0.006), New York Heart Association classification (NYHA) IV heart failure (P = 0.003) and metastasised cancer disease (P = 0.0002). Serum FT(3) values correlated inversely with serum C-reactive protein (P < 0.0001), lactate dehydrogenase (P = 0.0004), fibrinogen (P = 0.03) and erythrocyte sedimentation rate (P < 0.0001) values, and progressively decreased with increasing tertiles of age (P = 0.0004). The mortality rate was significantly higher (P = 0.0002) among patients with low T3 syndrome, which emerged as the sole predictive factor of death (odds ratio 4.3; 95% confidence interval 1.7-10.5). CONCLUSIONS: low T3 syndrome is very common in the hospitalised older population, emerging as the most sensitive independent predictor of short-term survival. Serum FT(3) determination should be included in the assessment of short-term prognosis of acutely ill older patients
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