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41.
A. I. Sozutov 《Proceedings of the Steklov Institute of Mathematics》2007,257(1):S181-S188
The theorems of Jordan, Frobenius, M. Hall, Brauer-Suzuki-Wall, Shunkov, Mazurov, and Belyaev are generalized. 相似文献
42.
It is proved that some groups with a strongly isolated 2-subgroup of period not exceeding four are locally finite. In particular,
the positive answer to Shunkov’s question 10.76 in the Kourovka notebook is obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 272–285, August, 2000. 相似文献
43.
A proper subgroup H of a group G is said to be strongly isolated if it contains the centralizer of any nonidentity element of H and 2-isolated if the conditions >C
G(g) H 1 and 2(CG(g)) imply that CG(g)H. An involution i in a group G is said to be finite if |ii
g| < (for any g G). In the paper we study a group G with finite involution i and with a 2-isolated locally finite subgroup H containing an involution. It is proved that at least one of the following assertions holds:1) all 2-elements of the group G belong to H;2) (G,H) is a Frobenius pair, H coincides with the centralizer of the only involution in H, and all involutions in G are conjugate;3) G=FFCG(i) is a locally finite Frobenius group with Abelian kernel F;4) H=V D is a Frobenius group with locally cyclic noninvariant factor D and a strongly isolated kernel V, U=O2(V) is a Sylow 2-subgroup of the group G, and G is a Z-group of permutations of the set =U
g g G. 相似文献