Geodesic
Subsocles Supporting Isotype and Balanced Subgroups
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 419-425

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1993-057-x
Mots-clés : 20K10, 20K27 
Hill, Paul; Megibben, Charles. Subsocles Supporting Isotype and Balanced Subgroups. Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 419-425. doi: 10.4153/CMB-1993-057-x
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