Matches in SemOpenAlex for { <https://semopenalex.org/work/W3199851987> ?p ?o ?g. }
- W3199851987 abstract "A group G is said to be n-centralizer if its number of element centralizers $$mid {{,mathrm{Cent},}}(G)mid =n$$ , an F-group if every non-central element centralizer contains no other element centralizer and a CA-group if all non-central element centralizers are abelian. For any non-abelian n-centralizer group G, we prove that $$mid frac{G}{Z(G)}mid le (n-2)^2$$ , if $$n le 12$$ and $$mid frac{G}{Z(G)}mid le 2(n-4)^{{log}_2^{(n-4)}}$$ otherwise, which improves an earlier result. We prove that if G is an arbitrary non-abelian n-centralizer F-group, then gcd $$(n-2, mid frac{G}{Z(G)}mid ) ne 1$$ . For a finite F-group G, we show that $$mid {{,mathrm{Cent},}}(G)mid ge frac{mid G mid }{2}$$ iff $$G cong A_4 $$ , an extraspecial 2-group or a Frobenius group with abelian kernel and complement of order 2. Among other results, for a finite group G with non-trivial center, it is proved that $$mid {{,mathrm{Cent},}}(G)mid = frac{mid G mid }{2}$$ iff G is an extraspecial 2-group. We give a family of F-groups which are not CA-groups and extend an earlier result." @default.
- W3199851987 created "2021-09-27" @default.
- W3199851987 creator A5073845223 @default.
- W3199851987 date "2022-06-29" @default.
- W3199851987 modified "2023-09-25" @default.
- W3199851987 title "Characterizations of Some Groups in Terms of Centralizers" @default.
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- W3199851987 doi "https://doi.org/10.1007/s00025-022-01687-4" @default.
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