On nilpotency of higher commutator subgroups of a finite soluble group
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DOI: 10.1007/s00013-020-01514-8
Abstract: Let G be a finite soluble group and $$G^{(k)}$$ G ( k ) the k th term of the derived series of G . We prove that $$G^{(k)}$$ G ( k ) is nilpotent if… read more here.
Keywords: higher commutator; finite soluble; nilpotency higher; soluble group ... See more keywords
On the Characterization of the Core of a π-Prefrattini Subgroup of a Finite Soluble Group
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DOI: 10.1134/s0037446619010063
Abstract: Let π be a set of primes and let H be a π-prefrattini subgroup of a finite soluble group G. We prove that there exist elements x, y, z ∈ G such that H ∩… read more here.
Keywords: prefrattini subgroup; soluble group; subgroup finite; finite soluble ... See more keywords
On σ-Residuals of Subgroups of Finite Soluble Groups
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DOI: 10.3390/math11102343
Abstract: Let σ={σi:i∈I} be a partition of the set of all prime numbers. A subgroup H of a finite group G is said to be σ-subnormal in G if H can be joined to G by… read more here.
Keywords: finite soluble; subgroup; subgroups finite; soluble groups ... See more keywords