Equation 677 Database

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Magma 6c6b18b8285b…

magma 6c6b18b8285b
Size
707
Isomorphism class hash
6c6b18b8285b6c6e8712464093c6b7e3f8ff2bcfe6119d0808a131cd68466123
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 20:17:10
Display reorder
498,497,496,493,494,495,611,293,292,288,289,290,291,165,166,167,162,163,164,93,92,94,95,90,91,54,59,55,56,57,58,86,85,87,88,89,84,103,102,104,105,106,107,196,195,197,192,193,194,23,22,18,19,20,21,176,175,177,178,179,174,282,283,284,285,286,287,303,302,304,305,301,300,434,433,432,437,435,436,333,335,334,332,331,330,519,518,517,521,522,520,533,535,534,538,536,537,362,361,360,365,363,364,515,514,516,513,511,512,594,593,595,596,597,598,586,585,584,588,589,587,529,532,592,531,591,530,607,620,643,606,633,632,631,645,647,698,667,680,699,679,700,696,689,702,705,706,82,81,83,78,79,80,187,188,189,190,191,186,114,119,115,116,117,118,181,180,182,183,184,185,120,125,121,122,123,124,205,204,206,207,208,209,216,221,217,218,219,220,237,236,238,239,234,235,245,244,240,241,242,243,68,67,69,70,71,66,53,52,48,49,50,51,371,370,369,368,366,367,349,348,350,351,352,353,569,570,568,573,571,572,417,419,418,416,414,415,422,421,420,425,423,424,374,373,372,375,376,377,459,458,457,461,462,460,413,412,411,409,410,408,390,392,391,393,394,395,623,622,624,626,648,650,629,642,630,681,682,690,683,663,674,666,669,677,688,697,269,268,264,265,266,267,16,17,12,13,14,15,24,29,25,26,27,28,222,227,223,224,225,226,144,149,145,146,147,148,252,257,253,254,255,256,2,0,3,4,5,1,10,9,11,6,7,8,171,170,172,173,168,169,251,250,246,247,248,249,263,262,258,259,260,261,564,563,562,567,565,566,468,467,466,464,465,463,523,525,524,528,526,527,475,477,476,480,478,479,502,504,503,499,500,501,605,604,603,600,601,602,453,452,451,455,456,454,483,482,481,485,486,484,543,542,544,540,541,539,616,646,617,644,621,627,639,638,628,691,684,687,692,657,673,675,658,693,685,701,270,272,274,273,271,275,155,150,151,152,153,154,34,33,35,30,31,32,311,310,306,307,308,309,134,133,135,136,137,132,313,312,314,315,316,317,295,294,296,297,298,299,138,143,139,140,141,142,45,44,46,47,42,43,281,280,276,277,278,279,41,40,36,37,38,39,471,470,469,474,472,473,407,406,405,403,404,402,385,384,386,387,388,389,398,397,396,400,401,399,447,449,448,444,445,446,506,505,507,510,508,509,379,378,380,381,382,383,488,487,489,490,491,492,555,554,553,552,550,551,609,608,615,614,612,613,610,651,649,703,671,676,704,660,665,678,659,686,695,694,111,110,112,113,108,109,229,230,231,232,233,228,210,215,211,212,213,214,157,156,158,159,160,161,326,328,327,324,325,329,128,127,129,130,131,126,198,203,199,200,201,202,320,318,321,322,323,319,65,64,60,61,62,63,75,74,76,77,72,73,101,100,96,97,98,99,441,443,442,438,439,440,580,578,579,582,583,581,599,450,574,575,576,577,356,355,354,358,359,357,558,557,556,561,559,560,590,549,548,545,546,547,341,340,339,337,338,336,428,427,426,430,431,429,342,344,343,345,346,347,634,635,636,618,637,619,641,625,640,672,656,664,670,654,652,655,653,662,661,668 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = {108, 109, 110, 111, 112, 113, 128} 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 20:17:12 · history