Results 1 to 10 of about 787,745 (111)
Self-normalizing Sylow subgroups [PDF]
Proceedings of the American Mathematical Society, 2003 Using the classification of finite simple groups we prove the following statement: Let p > 3 p>3 be a prime, Q Q a group of automorphisms of p p -power order of a finite group G G , and P P a Q Q -invariant Sylow
Guralnick, Robert M. +2 more
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Normal Subgroups Contained in the Frattini Subgroup [PDF]
Proceedings of the American Mathematical Society, 1972 Let H be a normal subgroup of the finite group G. If H has a subgroup K which is normal in G, satisfies | K | > | K ∩ Z 1 ( H ) | = p |K| &
Hill, W. Mack, Wright, Charles R. B.
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, 2020 10 pages; to appear in DMTCS Proceedings (Formal Power Series and Algebraic Combinatorics)
Arreche, Carlos E., Williams, Nathan F.
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Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem [PDF]
, 2001 In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups, finding hidden
Ivanyos, Gabor +2 more
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Centers of subgroups of big mapping class groups and the Tits alternative [PDF]
, 2019 In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups.
Lanier, Justin, Loving, Marissa
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Maximal Compact Normal Subgroups [PDF]
Proceedings of the American Mathematical Society, 1987 A locally compact group G has a maximal compact subgroup if and only if \(G/G_ 0\) has a maximal compact subgroup (Theorem 1). In a totally disconnected locally compact group (such as \(G/G_ 0\) above), every compact subgroup is contained in an open compact subgroup; in particular, maximal compact subgroups are necessarily open.
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Centralizers of normal subgroups and the $Z^*$-Theorem [PDF]
, 2015 Glauberman's $Z^*$-theorem and analogous statements for odd primes show that, for any prime $p$ and any finite group $G$ with Sylow $p$-subgroup $S$, the centre of $G/O_{p^\prime}(G)$ is determined by the fusion system $\mathcal{F}_S(G)$.
Henke, Ellen, Semeraro, Jason
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Subgroups close to normal subgroups
Journal of Algebra, 1989 Let G be a group and H a subgroup. It is shown that the set of indices \(\{\) [H: \(H\cap gHg^{-1}]|\) \(g\in G\}\) has a finite upper bound n if and only if there is a normal subgroup \(N\trianglelefteq G\) which is commensurable with H; i.e., such that [H:N\(\cap H]\) and [N:N\(\cap H]\) are finite; moreover, the latter indices admit bounds depending
Lenstra, H.W., Bergman, G.
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Normal Subgroups Contained in Frattini Subgroups are Frattini Subgroups [PDF]
Proceedings of the American Mathematical Society, 1980 We prove that if N is a normal subgroup of the finite group G and if N ⊆ Φ ( G ) N \subseteq \Phi (G) , then there exists a finite group U such that N = Φ ( U ) N = \Phi (U) exactly.
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Some normal subgroups of homomorphisms [PDF]
Transactions of the American Mathematical Society, 1966 lement of a euclidean neighborhood, and for B the closure of a euclidean neighborhood. They are able to show that the set of h which satisfy (a) is just the group P(X) generated by the elements of H(X) which agree with the identity on some open set, provided X has what they call a stable structure.
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