Equation 677 Database

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Magma c0ab119de33c…

magma c0ab119de33c
Size
381
Isomorphism class hash
c0ab119de33c51373865041acecc05ad2895ff89f9a95ccad9a4180e709e3a68
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 23:18:20
Display reorder
380,314,313,312,316,317,315,58,63,53,43,48,38,99,104,94,8,299,9,88,278,83,73,78,68,162,167,172,177,182,187,247,252,257,262,267,272,120,125,131,107,112,116,17,292,12,27,32,20,217,222,227,232,237,242,157,146,151,140,135,281,202,192,197,212,207,287,337,332,367,358,376,352,349,342,362,373,318,320,319,323,321,322,55,61,50,41,46,35,98,102,93,5,297,4,86,275,81,70,75,65,160,165,170,176,181,186,246,251,256,260,265,270,123,128,133,108,113,118,16,290,11,26,31,24,216,221,226,230,235,240,155,145,150,141,136,280,200,190,195,210,206,285,335,331,365,355,378,350,347,340,360,371,304,303,305,301,300,302,59,64,54,44,49,39,97,101,91,1,296,3,89,279,84,74,79,69,163,168,173,178,183,188,249,254,259,264,269,274,121,126,130,106,111,115,19,294,14,29,34,23,219,224,229,234,239,244,158,148,153,143,138,282,204,194,199,214,209,289,339,333,369,359,375,354,346,344,363,374,310,309,311,306,307,308,56,60,51,40,45,36,96,100,92,2,295,0,85,276,80,71,76,66,164,169,174,179,184,189,248,253,258,263,268,273,122,127,132,105,110,117,18,293,13,28,33,22,218,223,228,233,238,243,159,149,154,144,139,283,203,193,198,213,208,288,338,334,368,356,377,353,345,343,364,370,326,325,324,328,329,327,57,62,52,42,47,37,95,103,90,7,298,6,87,277,82,72,77,67,161,166,171,175,180,185,245,250,255,261,266,271,124,129,134,109,114,119,15,291,10,25,30,21,215,220,225,231,236,241,156,147,152,142,137,284,201,191,196,211,205,286,336,330,366,357,379,351,348,341,361,372 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {73} 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 23:18:21 · history