Equation 677 Database

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Magma af804d8da3e8…

magma af804d8da3e8
Size
707
Isomorphism class hash
af804d8da3e88ce5bec2eb9e0dc89a89b8381d7a7adfae9d345efac8af2ea2d6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 09:59:18
Display reorder
437,436,435,439,440,438,634,81,80,82,83,78,79,49,50,51,52,53,48,113,112,108,109,110,111,210,215,211,212,213,214,228,233,229,230,231,232,245,244,241,240,242,243,72,77,73,74,75,76,237,236,238,239,235,234,121,120,122,123,124,125,216,221,217,218,219,220,317,316,313,312,314,315,528,530,529,526,527,525,396,398,397,393,394,395,501,503,502,504,505,506,404,403,402,399,400,401,390,392,391,387,388,389,477,479,478,480,481,482,485,484,483,486,487,488,347,346,345,343,344,342,522,524,523,519,520,521,608,609,611,612,607,610,638,645,647,699,670,679,697,676,696,698,688,704,705,706,16,15,17,12,13,14,255,256,257,252,253,254,246,251,247,248,249,250,114,119,115,116,117,118,295,299,294,296,297,298,66,71,67,68,69,70,84,89,85,86,87,88,95,94,90,91,92,93,98,97,99,100,101,96,19,18,20,21,22,23,209,208,204,205,206,207,509,508,507,510,511,512,571,572,570,573,574,575,385,384,386,382,383,381,419,418,417,420,421,422,495,497,496,498,499,500,425,424,423,428,426,427,494,493,492,489,490,491,593,592,591,588,590,589,577,578,576,579,580,581,637,639,635,632,648,649,642,636,640,683,680,687,681,657,665,666,671,682,691,700,131,130,126,127,128,129,161,156,157,158,159,160,265,269,264,266,267,268,33,32,34,35,30,31,38,37,39,40,41,36,143,142,138,139,140,141,134,133,135,136,137,132,187,186,188,189,190,191,184,183,185,180,181,182,162,167,163,164,165,166,174,179,175,176,177,178,430,429,431,434,432,433,447,449,448,450,451,452,560,558,559,563,561,562,445,444,446,443,441,442,602,600,601,605,603,604,338,337,336,341,339,340,538,537,539,536,535,534,453,455,454,458,456,457,583,584,582,585,586,587,613,646,614,644,616,615,631,641,643,692,678,690,694,659,669,677,660,693,684,701,280,279,281,276,277,278,275,270,271,272,273,274,1,5,0,2,3,4,309,308,310,311,306,307,172,171,173,168,169,170,300,301,302,303,304,305,44,43,45,46,47,42,103,102,104,105,106,107,198,203,199,200,201,202,28,27,29,24,25,26,260,258,261,262,263,259,465,467,466,469,470,468,543,542,544,540,541,545,565,566,564,567,568,569,555,557,556,552,554,553,371,370,369,368,366,367,373,372,374,376,377,375,546,547,548,551,549,550,533,532,531,380,378,379,595,596,594,597,598,599,627,606,626,629,633,628,630,651,650,702,668,675,703,661,667,685,664,689,686,695,6,11,7,8,9,10,196,197,192,193,194,195,155,154,150,151,152,153,225,224,226,227,222,223,326,328,327,324,325,329,291,290,289,292,293,288,63,62,64,65,60,61,320,318,321,322,323,319,146,145,147,148,149,144,55,54,56,57,58,59,286,285,287,283,282,284,415,414,416,413,411,412,410,409,408,407,405,406,464,463,462,461,459,460,357,359,358,355,356,354,330,331,332,334,335,333,361,360,362,364,365,363,352,351,353,350,348,349,514,513,515,516,517,518,472,471,473,475,476,474,618,620,619,622,623,621,617,624,625,674,656,663,672,653,652,655,654,662,658,673 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, M = {78, 79, 80, 81, 82, 83, 133} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-08 09:59:19 · history