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Assume that G is a finite group, π(G) = {s} ∪ σ, s > 2, Σ is a set of Sylow σ-subgroups in which one subgroup is taken for each… Click to show full abstract
Assume that G is a finite group, π(G) = {s} ∪ σ, s > 2, Σ is a set of Sylow σ-subgroups in which one subgroup is taken for each pi 2 σ, and R(G) is the largest normal soluble subgroup in G (soluble radical of G). Moreover, suppose that each Sylow pi-subgroup Gpi ???? Σ normalizes the s-subgroup T(i) ≠ 1 of the group G. In this case, we establish the conditions under which s divides |R(G)|.
Keywords:
soluble radicals;
finite groups;
subgroup;
radicals finite
Journal Title: Ukrainian Mathematical Journal
Year Published: 2020
Link to full text (if available)
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Journal Title: Ukrainian Mathematical Journal
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!