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An involution i of a group G is said to be almost perfect in G if any two involutions of iG the order of a product of which is infinite are conjugated via a suitable involution in iG. We generalize a known result by Brauer, Suzuki, and Wall concerning the structure of finite groups with elementary Abelian
centralizers of involutions to groups with almost perfect involutions.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 75–82, January–February, 2007. 相似文献
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V. M. Sitnikov 《Mathematical Notes》1971,10(4):685-690
Finite nonsolvable groups are described whose involution centralizers are 2-closed or 2-closed, whereas the Sylow p-subgroups for p>2 are cyclic.Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 437–446, October, 1971.In conclusion, the author expresses his gratitude to A. I. Starostin for posing the problem and for scientific guidance. 相似文献
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Let FH be a supersolvable Frobenius group with kernel F and complement H. Suppose that a finite group G admits FH as a group of automorphisms in such a manner that and is nilpotent of class c. We show that G is nilpotent of -bounded class. 相似文献
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Given a positive integer m and a group-word w, we consider a finite group G such that $$w(G) \ne 1$$ and all centralizers of non-trivial w-values have order at most m. We prove that if $$w=v(x_1^{q_1},\dots ,x_k^{q_k})$$, where v is a multilinear commutator word and $$q_1, \dots , q_k$$ are p-powers for some prime p, then the order of G is bounded in terms of w and m only. Similar results hold when w is the nth Engel word or the word $$w=[x^n, y_1, \dots ,y_k]$$ with $$k \ge 1$$. 相似文献
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V. I. Senashov 《Mathematical Notes》1997,62(4):480-487
The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary
ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that
of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic
groups, and a generalized Chernikov group is a layer-finite extension of a direct productA of quasi-cyclicp-groups with finitely many factors for each primep such that each of its elements does not commute elementwise with only finitely many Sylow subgroups ofA. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved.
Translated fromMatematicheskie Zametki, Vol. 62, No 4, pp. 577–587, October, 1997.
Translated by A. I. Shtern 相似文献
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B. A. Kramarev 《Mathematical Notes》1977,21(3):165-167
We consider topological groups in which the centralizer of any element is invariant. We prove that these and only these groups are 2-Engel groups.Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 297–300, March, 1977. 相似文献
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