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Start Over Coverage 819-826

1. Characterizing projective general unitary groups ${\rm PGU}_3(q^2)$ by their complex group algebras

Creator:
Shirjian, Farrokh and Iranmanesh, Ali
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
character degree, complex group algebra, projective general unitary group, 13, and 51
Language:
English
Description:
Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary character table of $G$. We will show that if $X_1(G)=X_1({\rm PGU}_3(q^2))$, then $G \cong{\rm PGU}_3(q^2)$. As a consequence, we show that the projective general unitary groups ${\rm PGU}_3(q^2)$ are uniquely determined by the structure of their complex group algebras., Farrokh Shirjian, Ali Iranmanesh., and Obsahuje bibliografické odkazy
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Linear operators that preserve graphical properties of matrices: isolation numbers

Creator:
Beasley, LeRoy B., Song, Seok-Zun, and Jun, Yizng Bae
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Boolean matrix, Boolean rank, Boolean linear operator, and isolation number
Language:
English
Description:
Let $A$ be a Boolean $\{0,1\}$ matrix. The isolation number of $A$ is the maximum number of ones in $A$ such that no two are in any row or any column (that is they are independent), and no two are in a $2\times 2$ submatrix of all ones. The isolation number of $A$ is a lower bound on the Boolean rank of $A$. A linear operator on the set of $m\times n$ Boolean matrices is a mapping which is additive and maps the zero matrix, $O$, to itself. A mapping strongly preserves a set, $S$, if it maps the set $S$ into the set $S$ and the complement of the set $S$ into the complement of the set $S$. We investigate linear operators that preserve the isolation number of Boolean matrices. Specifically, we show that $T$ is a Boolean linear operator that strongly preserves isolation number $k$ for any $1\leq k\leq \min \{m,n\}$ if and only if there are fixed permutation matrices $P$ and $Q$ such that for $X\in {\mathcal M}_{m,n}(\mathbb B)$ $T(X)=PXQ$ or, $m=n$ and $T(X)=PX^tQ$ where $X^t$ is the transpose of $X$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public