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Given integers $k,l\geq 2$, where either $l$ is odd or $k$ is even, let $n(k,l)$ denote the largest integer $n$ such that each element of $A_n$ is a product of $k$ many $l$-cycles. In 2008, M. Herzog, G. Kaplan and A. Lev proved that if $k,l$ both ar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b310051b7a4cdeb1f6994de08dcbb648
Autor:
Rijubrata Kundu, Sumit Chandra Mishra
In this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset of the centralizer of an involution in a finite non-abelian simple group $G$ contains an odd order element, unless $G=\text{PS
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::614d376fb4e2fd1bae6f63bd1cf735cc