Equation 677 Database

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Magma 5663206e9980…

magma 5663206e9980
Size
595
Isomorphism class hash
5663206e998004ecb54c7d9fe809ca72849a0f8f434b967862d5cd40cd1c1700
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 12:20:48
Display reorder
74,73,75,76,77,72,306,311,307,308,309,310,372,371,379,369,370,368,328,327,326,325,323,324,395,394,393,396,397,398,511,525,514,553,594,221,216,217,218,219,220,2,0,3,4,5,1,266,265,267,268,269,264,212,211,213,214,215,210,10,9,11,6,7,8,242,241,243,244,245,240,57,56,58,59,54,55,26,25,27,28,29,24,30,35,31,32,33,34,128,127,129,130,131,126,356,355,354,358,359,357,382,381,380,383,384,385,389,391,390,386,387,388,317,316,318,320,375,319,489,490,509,508,487,488,322,465,426,463,425,464,526,531,527,528,522,523,543,578,563,555,551,564,583,581,554,573,189,190,191,186,187,188,233,232,228,229,230,231,21,20,22,23,18,19,37,36,38,39,40,41,50,49,51,52,53,48,16,15,17,12,13,14,161,160,156,157,158,159,235,234,236,237,238,239,172,171,173,168,169,170,111,110,112,113,108,109,459,458,419,497,501,496,466,500,467,469,470,468,507,486,499,485,447,446,493,453,452,433,434,432,407,406,408,410,411,409,321,460,423,461,424,462,534,541,510,540,513,539,576,560,566,558,587,577,590,557,549,591,222,223,224,225,226,227,181,180,182,183,184,185,274,273,275,270,271,272,163,162,164,165,166,167,176,175,177,178,179,174,104,103,105,106,107,102,145,144,146,147,148,149,67,66,68,69,70,71,154,153,155,150,151,152,194,193,195,196,197,192,334,333,335,330,331,332,402,401,400,403,404,405,340,339,341,337,338,336,373,312,313,315,374,314,471,472,504,329,505,473,474,342,475,506,476,343,535,536,518,517,519,516,567,565,561,569,584,545,585,574,570,575,45,46,47,42,43,44,284,283,285,286,287,282,100,99,101,96,97,98,115,114,116,117,118,119,199,198,200,201,202,203,94,93,95,90,91,92,85,84,86,87,88,89,256,255,257,252,253,254,125,124,120,121,122,123,79,78,80,81,82,83,479,431,430,352,353,351,367,366,365,412,363,364,413,415,414,416,417,454,457,495,418,494,455,456,349,348,350,346,347,345,422,420,502,498,503,421,524,532,533,521,542,520,588,562,571,547,552,580,548,550,546,544,136,137,132,133,134,135,208,207,209,204,205,206,246,251,247,248,249,250,263,262,258,259,260,261,60,65,61,62,63,64,295,294,296,297,298,299,301,300,302,303,304,305,140,139,141,142,143,138,278,277,279,280,281,276,289,288,290,291,292,293,492,451,450,448,449,491,478,429,428,344,427,477,445,444,443,442,440,441,437,481,392,480,436,435,377,376,360,361,362,378,399,482,438,483,439,484,537,538,529,530,512,515,572,592,559,593,586,556,579,582,589,568 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = the submagma generated by {54, 60} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 12:20:50 · history