Унiтарнi пiдгрупи комутативних групових алгебр характеристики 2

В. Лавер; Ж.  Балог

doi:10.37863/umzh.v72i6.1068

В. Лавер Ужгород. нац. ун-т https://orcid.org/0000-0001-6627-2445
Ж. Балог Ун-т Об’єднаних Арабських Емiратiв, Аль-Айн https://orcid.org/0000-0001-5908-3443

DOI: https://doi.org/10.37863/umzh.v72i6.1068

Анотація

УДК 512.552.7

Нехай $FG$ — групова алгебра скiнченної 2-групи $G$ над скiнченним полем $F$ характеристики 2 i $\circledast$ — iнволюцiя, що виникає iз групи $G$. $\circledast $ - унiтарна пiдгрупа $FG$, яка позначається $V_{\circledast}(FG)$, визначається, як множина всiх нормалiзованих одиниць $u$, якi задовольняють властивiсть $u^{\circledast}=u^{-1}$.
У данiй статтi знайдено порядок $V_{\circledast}(FG)$ для всiх iнволюцiй $\circledast$ , якi виникають iз $G$, де $G$ — скiнченна циклiчна 2-група, i показано, що всi $\circledast$ -унiтарнi пiдгрупи $FG$ неiзоморфнi.

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