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Factorizations of locally finite groups. (English. Russian original) Zbl 0598.20034

Sib. Math. J. 21, 890-897 (1981); translation from Sib. Mat. Zh. 21, No. 6, 186-195 (1980).
Main results: Theorem 1. Let the group G be locally finite and factorizable by locally normal subgroups A and B, \(\pi\) a set of primes, P and Q invariant Sylow \(\pi\)-subgroups of A and B, respectively. Then if G is locally solvable or the set \(\pi\) consists of a single prime, P and Q commute with one another and the product \(P\cdot Q\) is a Sylow \(\pi\)- subgroup of G. Furthermore, every finite \(\pi\)-subgroup of G is contained in some subgroup conjugate in G to \(P\cdot Q\). Theorem 2. Let G be a locally finite group which is factorized by two almost locally normal subgroups which satisfy the minimal condition for p-subgroups (p a prime). Then G also satisfies the minimal condition for p-subgroups.

MSC:

20E15 Chains and lattices of subgroups, subnormal subgroups
20E25 Local properties of groups
20E07 Subgroup theorems; subgroup growth
20F50 Periodic groups; locally finite groups
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References:

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