Equation 677 Database

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Magma a7e053ccd781…

magma a7e053ccd781
Size
707
Isomorphism class hash
a7e053ccd781e40c8a1be48f3b46dbe244edc5597cc471060feae20b267c92bf
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 00:38:14
Display reorder
361,362,585,360,381,359,628,59,58,54,55,56,57,155,150,151,152,153,154,224,223,225,226,227,222,242,240,243,244,245,241,229,228,230,231,232,233,146,145,147,148,149,144,246,247,248,249,250,251,125,124,120,121,122,123,51,50,52,53,48,49,42,47,43,44,45,46,305,304,301,300,302,303,469,471,470,472,473,474,468,467,466,464,465,463,453,452,451,455,456,454,545,544,546,541,542,543,435,434,433,438,436,437,338,340,339,336,337,335,589,588,587,591,598,590,519,518,517,520,521,522,596,595,597,593,594,592,611,639,643,640,610,612,635,645,647,699,671,682,700,681,696,697,692,703,705,706,206,205,207,208,209,204,141,142,143,138,139,140,234,239,235,236,237,238,115,114,116,117,118,119,129,128,130,131,126,127,289,288,290,291,292,293,258,263,259,260,261,262,264,269,265,266,267,268,257,256,252,253,254,255,10,9,11,6,7,8,105,104,106,107,102,103,447,446,445,450,448,449,348,347,349,350,351,352,486,485,484,482,483,481,505,507,506,510,508,509,404,403,405,407,408,406,475,477,476,479,480,478,523,525,524,528,526,527,487,489,488,491,492,490,575,576,574,577,578,579,615,618,617,616,648,649,625,642,624,676,677,694,684,664,673,674,672,683,686,698,287,286,282,283,284,285,77,72,73,74,75,76,180,185,181,182,183,184,276,281,277,278,279,280,190,189,191,186,187,188,23,22,18,19,20,21,97,96,98,99,100,101,34,33,35,30,31,32,135,134,136,137,132,133,275,274,270,271,272,273,12,17,13,14,15,16,330,331,332,586,334,333,389,388,390,385,386,387,443,442,444,439,440,441,513,512,511,515,516,514,345,344,346,342,343,341,605,604,603,600,601,602,501,500,499,503,504,502,569,568,570,573,571,572,539,538,540,536,537,535,626,646,627,644,629,613,631,630,623,695,680,689,691,658,666,679,660,690,678,701,164,163,165,166,167,162,197,192,193,194,195,196,27,26,28,29,24,25,306,311,307,308,309,310,41,40,36,37,38,39,313,312,314,315,316,317,298,297,299,294,295,296,110,109,111,112,113,108,156,161,157,158,159,160,81,80,82,83,78,79,3,2,4,5,1,0,409,411,410,412,413,414,418,420,419,417,415,416,402,401,400,398,399,397,364,363,365,366,367,368,424,426,425,421,422,423,561,560,559,557,556,558,567,566,565,562,564,563,353,355,354,357,358,356,493,495,494,496,497,498,622,621,614,620,607,608,619,651,650,702,665,685,704,662,667,675,661,687,688,693,178,177,179,174,175,176,211,212,213,214,215,210,221,220,216,217,218,219,203,202,198,199,200,201,326,328,327,324,325,329,168,173,169,170,171,172,64,63,65,60,61,62,320,318,321,322,323,319,67,66,68,69,70,71,85,84,86,87,88,89,91,90,92,93,94,95,427,429,428,430,431,432,462,461,460,458,459,457,599,583,584,580,581,582,531,530,529,533,534,532,547,549,548,550,551,552,553,555,554,383,384,382,380,379,378,376,377,375,392,391,393,396,394,395,374,373,372,371,369,370,609,636,606,634,638,637,632,641,633,670,656,659,668,653,652,655,654,657,663,669 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = {114, 115, 116, 117, 118, 119, 135} 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 00:38:15 · history