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A note on the Π -property of some subgroups of finite groups

Zhengtian Qiu, Guiyun Chen, Jianjun Liu (2024)

Czechoslovak Mathematical Journal

Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K ∩ L / K ) | is a π ( H K / K ∩ L / K ) -number. We obtain some criteria for the p -supersolubility or p -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the Π -property.

A note on uniserial loops

Jaroslav Ježek, Tomáš Kepka (2010)

Commentationes Mathematicae Universitatis Carolinae

All ordinal numbers α with the following property are found: there exists a loop such that its subloops form a chain of ordinal type α .

A note on weakly-supplemented subgroups and the solvability of finite groups

Xin Liang, Baiyan Xu (2022)

Czechoslovak Mathematical Journal

Suppose that G is a finite group and H is a subgroup of G . The subgroup H is said to be weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In this note, by using the weakly-supplemented subgroups, we point out several mistakes in the proof of Theorem 1.2 of Q. Zhou (2019) and give a counterexample.

A note on weakly-supplemented subgroups of finite groups

Hong Pan (2018)

Czechoslovak Mathematical Journal

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In the paper, we extend one main result of Kong and Liu (2014).

A parallelogram configuration condition in nets

Jitka Markvartová (1993)

Archivum Mathematicum

After describing a (general and special) coordinatization of k -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in k -nets with small degree k .

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