Weakly fully and characteristically inert socleregular Abelian p-groups A. R. Chekhlov, P. V. Danchev
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ArticleContent type: Текст Media type: электронный Subject(s): инертные цокольно-регулярные группы | абелевы p-группыGenre/Form: статьи в журналах Online resources: Click here to access online
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Communications in algebra Vol. 50, № 11. P. 4975-4987Abstract: In regard to two recent publications in the Mediterranean J. Math. (2021) and Forum Math. (2021) related to fully and characteristically inert socleregularity, respectively, we define and study the so-called weakly characteristically inert socle-regular groups. In that aspect, as a culmination of the investigations of this sort, some more global results are obtained and, moreover, some new concrete results concerning the weakly fully inert socle-regular groups, defined as in the firstly mentioned above paper, are also established. In particular, we prove that all torsion-complete groups are characteristically inert socle-regular, which encompasses an achievement from the secondly mentioned paper and completely settles the problem posed there about this class of groups.
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In regard to two recent publications in the Mediterranean J. Math. (2021) and Forum Math. (2021) related to fully and characteristically inert socleregularity, respectively, we define and study the so-called weakly characteristically inert socle-regular groups. In that aspect, as a culmination of the investigations of this sort, some more global results are obtained and, moreover, some new concrete results concerning the weakly fully inert socle-regular groups, defined as in the firstly mentioned above paper, are also established. In particular, we prove that all torsion-complete groups are characteristically inert socle-regular, which encompasses an achievement from the secondly mentioned paper and completely settles the problem posed there about this class of groups.
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