Equation 677 Database

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Magma 3a2eafbff633…

magma 3a2eafbff633
Size
707
Isomorphism class hash
3a2eafbff633bba415a66488902ee19e9ebb0286cc1c34b9b87d680be7616062
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 08:05:00
Display reorder
229,230,231,232,233,228,706,172,171,173,168,169,170,100,99,101,96,97,98,125,124,120,121,122,123,303,302,304,305,301,300,93,92,94,95,90,91,131,130,126,127,128,129,332,330,333,334,335,331,323,322,319,318,320,321,239,238,234,235,236,237,324,325,326,327,328,329,244,243,245,240,241,242,409,408,410,406,407,405,518,517,516,520,521,519,404,403,402,399,400,401,527,526,525,524,522,523,532,531,533,529,530,528,416,415,414,413,411,412,356,355,354,359,357,358,554,552,553,555,556,557,422,421,420,417,418,419,615,649,647,640,648,650,624,638,639,695,668,661,669,699,704,703,702,700,705,701,183,182,184,185,180,181,291,290,292,293,288,289,26,25,27,28,29,24,16,15,17,12,13,14,149,148,144,145,146,147,143,142,138,139,140,141,155,154,150,151,152,153,41,40,36,37,38,39,164,163,165,166,167,162,156,161,157,158,159,160,194,193,195,196,197,192,447,449,448,444,445,446,463,462,464,465,466,467,473,472,471,468,469,470,433,432,437,430,431,429,353,352,351,350,348,349,443,442,441,440,438,439,365,364,363,362,360,361,578,576,577,579,580,581,423,425,424,427,428,426,633,622,637,621,629,636,641,643,645,675,674,662,660,689,691,673,690,676,697,692,112,111,113,108,109,110,224,223,225,226,227,222,47,46,42,43,44,45,210,215,211,212,213,214,247,246,248,249,250,251,220,219,221,216,217,218,53,52,48,49,50,51,312,313,314,315,316,317,71,70,66,67,68,69,85,84,86,87,88,89,278,277,279,280,281,276,594,595,596,598,599,597,600,601,602,603,604,605,538,537,539,536,534,535,344,343,342,347,345,346,508,507,509,505,506,504,546,548,547,549,550,551,544,543,545,541,542,540,501,503,502,499,500,498,568,567,569,566,565,564,632,630,635,631,617,634,620,618,619,681,671,665,664,687,680,686,678,679,694,688,282,287,283,284,285,286,272,271,273,274,275,270,33,32,34,35,30,31,60,65,61,62,63,64,72,77,73,74,75,76,56,55,57,58,59,54,308,306,309,310,311,307,263,262,258,259,260,261,254,253,255,256,257,252,268,267,269,264,265,266,79,78,80,81,82,83,585,587,586,583,582,584,480,482,481,485,483,484,341,340,339,337,336,338,476,475,474,479,477,478,592,591,593,588,590,589,487,486,488,490,491,489,559,558,560,561,562,563,495,497,496,493,494,492,575,574,573,571,570,572,628,626,623,625,627,616,642,644,646,696,666,658,683,684,685,693,672,682,698,677,2,0,3,4,5,1,11,10,6,7,8,9,22,21,23,18,19,20,176,175,177,178,179,174,295,294,296,297,298,299,135,134,136,137,132,133,191,190,186,187,188,189,115,114,116,117,118,119,107,106,102,103,104,105,204,209,205,206,207,208,198,203,199,200,201,202,459,461,460,456,457,458,454,453,455,450,451,452,375,374,376,373,371,372,395,394,393,398,396,397,377,379,378,380,381,382,390,392,391,387,388,389,511,510,512,514,515,513,368,367,366,369,434,370,386,436,385,383,435,384,607,611,614,606,610,609,608,612,613,667,653,651,652,663,657,656,655,654,670,659 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {0, 1, 2, 3, 4, 5, 146} 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 08:05:01 · history