A note on the splitting length of a finite direct sum of mixed Abelian groups of rank one
All ordinal numbers with the following property are found: there exists a loop such that its subloops form a chain of ordinal type .
Suppose that is a finite group and is a subgroup of . The subgroup is said to be weakly-supplemented in if there exists a proper subgroup of such that . 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 subgroup of a finite group is weakly-supplemented in if there exists a proper subgroup of such that . In the paper, we extend one main result of Kong and Liu (2014).
The purpose of this paper is to give a general and a simple approach to describe the Sylow r-subgroups of classical groups.
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .