Equation 677 Database

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Magma 8190d6ffa77e…

magma 8190d6ffa77e
Size
451
Isomorphism class hash
8190d6ffa77e9a80ecac8f8fd8499038209e8554b4a1708af4776a2349214940
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 07:48:38
Display reorder
447,445,448,440,442,443,444,441,449,446,450,311,239,171,139,125,93,35,325,339,109,312,240,182,140,126,94,33,326,340,103,241,313,172,141,127,155,50,327,341,104,314,242,173,142,128,156,48,328,342,105,307,243,174,143,129,95,49,329,343,106,158,236,308,175,144,130,90,153,330,344,107,237,309,176,145,131,91,36,323,345,108,238,310,167,163,132,92,34,324,351,8,2,14,28,10,11,7,22,380,381,373,372,374,375,376,377,378,379,390,391,383,382,384,385,386,387,388,389,401,400,393,392,394,395,396,397,398,399,410,411,403,402,404,405,406,407,408,409,420,421,413,412,414,415,416,417,418,419,429,431,430,423,422,424,425,426,427,428,359,361,360,353,352,354,355,356,357,358,369,371,370,363,362,364,365,366,367,368,434,439,435,437,438,432,433,436,32,232,183,286,60,215,253,204,272,306,46,233,170,287,61,216,254,198,273,299,234,45,181,288,62,217,255,199,274,300,47,235,169,289,63,218,256,200,267,301,38,228,185,290,64,219,257,201,268,302,303,229,39,187,283,57,220,258,202,269,304,230,40,188,284,58,213,252,203,270,305,231,41,189,285,59,214,350,348,271,12,13,16,30,18,24,29,20,335,135,180,316,102,54,87,123,116,149,336,136,166,317,96,55,118,160,119,150,137,337,186,318,97,56,88,124,110,151,338,161,184,319,98,37,89,120,111,146,331,162,177,320,99,117,83,121,112,147,164,138,332,178,321,100,51,84,122,113,148,133,333,179,322,157,52,85,159,114,165,134,334,168,315,101,53,86,347,115,1,3,4,6,15,21,26,5,265,75,246,291,76,280,66,191,227,207,266,68,247,292,77,281,67,192,221,208,69,259,248,293,78,282,65,193,222,209,260,70,249,294,79,275,152,194,223,210,261,71,250,295,80,276,42,195,224,211,212,72,262,251,296,81,277,43,196,225,205,73,263,244,297,82,278,44,197,226,206,74,264,245,298,154,279,346,190,349,9,0,17,31,19,23,27,25 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#95b751a48b68a2f621632970f3421a3553e52ef647924d13ccb1c1f20c19d287, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + 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: 11.

last edited by qawbecrdtey at 2026-10-07 07:48:39 · history