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Questions about the branch of algebra that deals with groups.

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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 …
M. Zallaghi's user avatar
3 votes
1 answer
184 views

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 …
M. Zallaghi's user avatar
1 vote
1 answer
405 views

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 …
M. Zallaghi's user avatar
1 vote
0 answers
152 views

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 $$cd(G)=\{\chi(1)|\chi\in Irr(G)\}=\{1,f_1,\dots,f_n,d\}, \;\;n\gt0,$$ …
M. Zallaghi's user avatar
1 vote
0 answers
112 views

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, …
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