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- W2465004545 abstract "Abstract We identify a condition, which we refer to as cohesiveness , on a subgroup S of the socle G[p] — {x ∊ G : px = 0} of an abelian p -group G which is necessary for S to be the socle of an isotype subgroup of G . It is shown, when S is countable, that this condition is both necessary and sufficient. A further restriction, definable in terms of the coset valuation on G/S , leads to the notion of S being completely cohesive in G . When S is countable, this latter condition is both necessary and sufficient for S to serve as the socle of a balanced subgroup of G . Also noteworthy is the fact that if H and K are, respectively, balanced and isotype subgroups of G with H[p] = K[p] , then K is necessarily balanced in G ." @default.
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- W2465004545 date "1993-12-01" @default.
- W2465004545 modified "2023-10-06" @default.
- W2465004545 title "Subsocles Supporting Isotype and Balanced Subgroups" @default.
- W2465004545 doi "https://doi.org/10.4153/cmb-1993-057-x" @default.
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