Factorizations of locally finite groups

Chernikov, N. S.

doi:10.1007/bf00968480

Cited by 3 publications

(4 citation statements)

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“…By [5], Theorem 5.8, p. 172, A*C/C and B*C/C are Cernikov groups. Hence by [4], Theorem 4, X/C is a soluble Cernikov group. Since X/C is the product of two âf-subgroups, it is an $6-group by [2], Lemma 3.1, p. 9.…”

Section: In Particularmentioning

confidence: 88%

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Factorized Groups with max, min and min-p

Amberg

1984

Can. math. bull.

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Let be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.

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Section: In Particularmentioning

confidence: 88%

“…It follows that A is a Cernikov group, so that also B -A is a Cernikov group. By [4], Theorem 4, G is a Cernikov group. Since 6 V >(G) is finite, G is an almost-p group.…”

Section: In Particularmentioning

confidence: 96%

Factorized Groups with max, min and min-p

Amberg

1984

Can. math. bull.

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“…The group G/T is soluble (See [15]), Part 2, Lemma 10.39), and so the setoff primes (G/T)  is finite by Lemma 4.1.5 of [5] (See also [15]). It follows from Lemma 4.1.4 of [4] (See also [15]) that there exists in G a normal series of finite length…”

Section: K  mentioning

confidence: 99%

“…This combines theorems of B. Amberg (see [1][2][3][4] and [6]) , N.S. Chernikov (see [5]), S. Franciosi, F. de Giovanni (see [3,6,[32][33][34][35][36]), O.H.Kegel (see [8]), J.C.Lennox (see [12]) , D.J.S. Robinson(see [9] and [15]), J.E.…”

Section: Introductionmentioning

confidence: 99%