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Results tagged with gr.group-theory
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user 42611
Questions about the branch of algebra that deals with groups.
1
vote
1
answer
405
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Are there any groups $G$ with the property $(*_d)$?
Let $G$ be a finite group of even order which has only one non-principal irreducible character $\chi$ of degree $d$, $d\in \mathbb{N}$, with the following property (we name it $(*_d)$):
$(*_d)$: Ther …
- 255
1
vote
0
answers
112
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We know $A_5$ as a non-CI-group. Now, is $A_5$ a BI-group?
We call a group satisfying the following property for all $\nu \in cd(G)$ (Irreducible character degrees of $G$) a BI-group (Babai Invariant group)
Let $G$ be a finite group, let $\Gamma=Cay(G, …
- 79
3
votes
1
answer
184
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Is there a characterization of CI-groups of order less than 100?
We know some benefit criterion in articles such as:
C. H. Li, On isomorphisms of finite Cayley graphs-a survey, Discrete Math., 256 (2002) 301-334.
C. H. Li, Z. P. Lu, P. P …
- 12.7k
1
vote
0
answers
152
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Do you know any clear classification of groups in which there would exist a unique non-linea...
According to
Lev Kazarin, On Thompson’s Theorem, Journal of Algebra 220, 574–590 (1999)
we know that:
[Corollary 5.3]:Let $$cd(G)=\{\chi(1)|\chi\in Irr(G)\}=\{1,f_1,\dots,f_n,d\}, \;\;n\gt0,$$ …
- 79
0
votes
Does the Alternating group of degree $n>7$ have exactly one irreducible character of degree ...
Uniqueness.
With respect to the proposition 20.13 provided in the book Representations and characters of groups by James and Liebeck, and the answer given above by Nick Gill, the uniqueness of the "i …
- 79