1,355,179 research outputs found
Semigroups with certain finiteness conditions and Chernikov groups
No full textThe main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open. © Journal "Algebra and Discrete Mathematics"
Semigroups with certain finiteness conditions and Chernikov groups
No full textThe main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open.English version of the paper published in Russian in the book “Algebra and Linear Inequalities. To the Centennial of the Birthday of S. N. Chernikov”, Ekaterinburg, 2012. Supported by the Russian Foundation for Basic Research, grant 10-01-00524
Semigroups with certain finiteness conditions and Chernikov groups
No full textThe main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open.English version of the paper published in Russian in the book “Algebra and Linear Inequalities. To the Centennial of the Birthday of S. N. Chernikov”, Ekaterinburg, 2012. Supported by the Russian Foundation for Basic Research, grant 10-01-00524
Locally finite groups containing a 2 -element with Chernikov centralizer
No full textSuppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ?g? has nilpotent centralizer, then G has a soluble subgroup of finite index.</p
Locally finite groups containing a 2 -element with Chernikov centralizer
No full textSuppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ?g? has nilpotent centralizer, then G has a soluble subgroup of finite index.</p
Her Altgrubu Altnormal Ya Da Nilpotent-By-Chernikov Olan Lokal Sonlu Gruplar
No full textBu tezde Howard SMITH'in Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov adlı makalesi çalışılmıştır. G her altgrubu altnormal ya da nilpotent-by-Chernikov olan lokal sonlu bir grup olsun. Eğer G sonlu üslü ise o zaman G nin nilpotent-by-sonlu olduğu gösterilmiştir. Ayrıca G nilpotent-by-Chernikov değilse o zaman G nin G(F,K)= A ⋊ K ya izomorf bir kesimi olduğu öyle ki A ve K sırasıyla lokal sonlu bir F cisminin toplamsal ve çarpımsal altgrupları olduğu ya da G(F,K) nin elemanter abelyen p-grup olduğu gösterilmiştir. Özel olarak K, A üzerine çarpımsal etki ederek F yi üretir.In this thesis, the paper written by Howard SMITH named Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov is studied. Let G is locally finite group satisfying all subgroups subnormal or nilpotent-by-Chernikov. It is shown that if G is finite exponent; then G is nilpotent-by-finite. Moreover, it is shown that if G is not nilpotent-by- Chernikov, then G has a section isomorphic to a group G(F,K) = A ⋊ K such that A and K is respectively additive and multicaptive subgroup of locally finite F field or that G(F,K) is elementary abelian p-group. In particular, K generates F by acting on A by multicaption
On periodic groups of Shunkov with the Chernikov centralizers of involutions
No full textLayer-finite groups for the first time appeared in the article of S.~N.~Chernikov (1945). Almost layer-finite groups are extensions of a layer-finite groups by finite groups. The author develops the direction of characterizations of known well studied classes of groups in other classes of groups with some additional (rather weak) finiteness conditions. In this paper almost layer-finite groups receive characterization in the class of periodic Shunkov groups. Shunkov group is a group in which for any of its finite subgroup~ in the factor group
any two conjugate elements of prime order generate a finite subgroup. We study periodic Shunkov's groups with the condition: normalizer of any finite non-unit subgroup is almost layer-finite. It is proved that if in such group the centralizers of involutions are Chernikov, then the group is almost layer-finite
Locally Nilpotent p-Groups Whose Proper Subgroups Are Hypercentral-by-Chernikov
No full textIf is a group theoretical property or class of groups then a group G is a -group if G has the property or is a member of the class Let G be a group andbe a property of groups. If every proper subgroup of G satisfies but G itsellf doesnot satisfy it, then G is called a minimal non- group (We denote the classes ofminimal non- group by -group). In this work we study locally nilpotent minimalnon- groups, where stands for hypercentral-by-Chernikov. It was shown in [1]that if N be a normal nilpotent subgroup and U be a nilpotent subnormal subgroup ofany group then NU is nilpotent. In this study, a generalizations of this situation wasgiven. Let N be a normal an N0 closed subgroup (see [2]) of G for a class N0-closed of groups and U be an N0-closed subnormal subgroup of G. Then UN isan N0-closed subgroup of G. In addition, the results for the nilpotent-byChernikovgroups of Asar [3] were also extended to hypercentral-by-Chernikov groupsin this study. Thus, the following results were obtained. Let G be a Baer p-group andevery proper subgroup is N0 closed -by-Chernikov for a class N0 closed . Thenevery proper subgroup of G which is generated by a subset of finite exponent is N0closed . Also we show that if G is a Baer p-group and G has a normal hypercentralN subgroup such that G/N Chernikov. Then G/N is nilpotent.Key Words: -group, -groups, hypercentral-by-Chernikov grup, Baregroup.REFERENCES[1] W. Möhres, Torsionsgruppen deren untergruppen alle subnormal Sind, Geom. Dedicata 31(1989), 237-244.International Conference on Mathematics and Mathematics Education(ICMME-2018), Ordu University, Ordu, 27-29 June 201873[2] D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups -Vols. I, II(Springer, Berlin).[3] A.O. ASAR, Locally nilpotent p- groups whose proper subgroups are hypercentral or nilpotentby- Chernikov. J.London Math. Soc., 61 (2000), 412-422.</p
Chernikov p-groups and integral p-adic representations of finite groups
No full textИзучается связь между p-группами Черникова и целочисленными р-адическими представле ниями конечных р-групп. Приводится описание с точностью до изоморфизма некоторых классов р-групп Черникова.The connection is studied between Chernikov p-groups and integral p-adic representations of finite p-groups. A description is presented with a precision up to isomorphism of certain classes of Chernikov p-groups.Вивчається зв’язок між р-групами Чернікова і цілочисловими р-адичними зображеннями скінченних р-груп. Описуються з точністю до ізоморфізму деякі класи р-груп Чернікова
Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov
No full textWe pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all subgroups subnormal or nilpotent-by-{C}hernikov. emph{Centr. Eur. J. Math.} (to appear)] of groups in which all subgroups are either subnormal or nilpotent-by-Chernikov. Denoting by the class of all such groups, our concern here is with locally finite p-groups in the class , where is a prime, while an earlier article provided a reasonable classification of locally finite nb-groups in which all of the p-sections are nilpotent-by-Chernikov. Our main result is that if is a Baer p-group in then is nilpotent-by-Chernikov
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