Equation 677 Database

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Magma 1e40304d9e26…

magma 1e40304d9e26
Size
707
Isomorphism class hash
1e40304d9e26235b77099a441385731765f02f6ca0db3141e8e112379b3d8727
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
2026-10-07 08:57:17
Display reorder
187,186,188,189,190,191,706,290,289,291,293,287,288,140,141,142,143,138,139,259,258,260,261,262,263,237,236,238,239,234,235,252,257,253,254,255,256,284,283,285,282,292,286,106,105,107,102,103,104,7,6,8,9,10,11,304,303,305,301,300,302,298,299,294,296,297,295,528,527,529,532,530,531,478,477,476,475,474,538,553,552,554,555,556,557,471,473,472,468,469,470,321,323,322,319,320,318,500,502,501,497,498,499,443,442,441,440,438,439,489,488,490,487,485,486,417,419,418,416,414,415,338,337,336,341,339,340,616,609,623,610,633,617,644,635,641,619,700,676,691,702,699,690,696,704,705,703,4,3,5,1,0,2,73,74,75,76,77,72,41,40,36,37,38,39,62,61,63,64,65,60,136,135,137,132,133,134,85,84,86,87,88,89,167,166,162,163,164,165,246,251,247,248,249,250,121,120,122,123,124,125,115,114,116,117,118,119,431,430,429,426,427,428,537,536,535,550,533,534,350,349,348,352,353,351,390,392,391,393,394,395,450,452,451,454,455,453,449,448,447,446,444,445,380,379,378,383,381,382,516,515,517,520,518,519,389,388,387,385,386,384,367,366,368,370,371,369,628,621,622,612,613,627,606,608,620,626,701,692,694,681,670,669,671,675,683,682,175,174,176,177,178,179,214,215,210,211,212,213,101,100,96,97,98,99,169,168,170,171,172,173,241,240,242,243,244,245,32,31,33,34,35,30,216,221,217,218,219,220,130,129,131,126,127,128,83,82,78,79,80,81,66,71,67,68,69,70,408,410,409,412,413,411,405,407,406,402,403,404,396,398,397,401,399,400,423,425,424,420,421,422,331,330,332,335,333,334,317,316,315,314,312,313,307,308,306,309,310,311,560,558,559,561,562,563,496,495,494,492,493,491,548,547,549,546,551,545,636,607,639,618,637,638,642,611,643,615,693,695,679,686,667,678,664,687,677,697,183,182,184,185,180,181,28,29,24,25,26,27,22,21,23,18,19,20,160,159,161,156,157,158,12,17,13,14,15,16,277,281,276,278,279,280,224,223,225,226,227,222,266,265,267,268,269,264,233,232,228,229,230,231,271,275,270,272,273,274,521,523,522,525,526,524,599,598,597,596,595,594,346,345,347,342,343,344,568,567,569,564,566,565,600,601,602,605,603,604,570,571,572,574,575,573,578,576,577,581,579,580,587,586,585,583,582,584,459,461,460,458,456,457,590,588,589,593,591,592,651,645,648,646,647,650,640,653,649,654,698,674,680,689,673,672,665,688,684,685,200,199,201,202,203,198,59,54,55,56,57,58,110,109,111,112,113,108,154,153,155,150,151,152,193,192,194,195,196,197,48,53,49,50,51,52,44,43,45,46,47,42,209,208,204,205,206,207,149,148,144,145,146,147,91,90,92,93,94,95,542,544,543,540,541,539,509,511,510,512,513,514,328,327,329,324,325,326,436,435,437,433,434,432,467,466,465,462,463,464,508,507,506,505,503,504,376,375,377,373,374,372,360,362,361,364,365,363,358,357,359,354,355,356,481,480,479,484,482,483,624,632,629,652,631,630,625,614,634,655,666,659,662,663,656,658,657,660,661,668 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 = {48, 49, 50, 51, 52, 53, 141} 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 2026-10-07 08:57:19 · history