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- W1511206154 abstract "S(G) is closed under the mapping (called the symmetry around s): χ->soχ= sx s (sy x^S(G)), and is a discrete symmetric space in the sense of [1], Let Φ (HyZ) be a central extension of G with the exact sequence 1->Z->H->G->1 where Z is contained in the center of H. Let r be an involution of H such that it leaves every element of Z invariant and φoτ=?σ oφ. In this case, we say that (H, Z; T) (or, (H, T)) is a central extension of the null type of (G, σ) . In this paper, a central extension implies that of the null type. It is easy to see that the symmetric core S(H) of (H, T) is homomorphic onto S(G), and we call S(H) a central extension, or, a covering (of the null type) of S(G). The main result obtained in this note is that there exists a generic covering S(U) of S(G) and S(U) is finite if G is finite. Here, a covering is called 'generic'' if every covering of S(G) is its homomorphic image. We also obtain some connections between the generic covering and the (restricted) Schur multiplier of G when G is finite." @default.
- W1511206154 created "2016-06-24" @default.
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- W1511206154 date "1993-09-01" @default.
- W1511206154 modified "2023-09-25" @default.
- W1511206154 title "Central extensions of the symmetric core of a group" @default.
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- W1511206154 doi "https://doi.org/10.18910/11228" @default.
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