Equation 677 Database

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Magma db61f127661b…

magma db61f127661b
Size
381
Isomorphism class hash
db61f127661b265a912b154e1830dcfde64f6a81ca11cf5e4460f59b9fa3b76c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:37:02
Display reorder
380,223,18,19,15,17,157,147,152,142,132,137,16,117,122,127,102,107,112,322,323,321,319,320,318,52,292,57,62,67,72,287,27,32,47,39,42,237,227,232,252,242,247,262,267,257,277,282,272,162,167,172,177,182,187,92,297,97,77,82,87,192,197,202,207,212,217,332,357,337,352,367,347,342,377,362,372,222,13,12,10,9,158,148,153,143,133,138,11,118,123,128,103,108,113,316,317,315,313,314,312,53,293,58,63,68,73,288,28,33,48,37,43,238,228,233,253,243,248,263,268,258,278,283,273,163,168,173,178,183,188,93,298,98,78,83,88,193,198,203,208,213,218,333,358,335,353,368,348,343,378,363,373,221,1,6,7,8,155,145,150,141,131,136,14,115,120,125,101,106,111,328,329,327,325,326,324,51,290,56,60,65,70,285,26,31,46,35,41,236,225,231,250,240,246,261,266,255,276,281,270,161,166,171,175,180,185,91,295,96,75,80,86,190,196,201,205,210,215,330,355,336,350,365,345,340,375,361,370,220,5,4,2,0,156,146,151,140,130,135,3,116,121,126,100,105,110,304,305,303,300,302,301,50,291,55,61,66,71,286,25,30,45,36,40,235,226,230,251,241,245,260,265,256,275,280,271,160,165,170,176,181,186,90,296,95,76,81,85,191,195,200,206,211,216,331,356,339,351,366,346,341,376,360,371,224,24,23,21,20,159,149,154,144,134,139,22,119,124,129,104,109,114,311,309,310,308,306,307,54,294,59,64,69,74,289,29,34,49,38,44,239,229,234,254,244,249,264,269,259,279,284,274,164,169,174,179,184,189,94,299,99,79,84,89,194,199,204,209,214,219,334,359,338,354,369,349,344,379,364,374 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {71} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:37:03 · history