Equation 677 Database

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Magma 91398eae94a8…

magma 91398eae94a8
Size
707
Isomorphism class hash
91398eae94a84a10781be6b6fbd5d432ebe4a5d62f1dcc166e9ffb290acfecee
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 16:57:27
Display reorder
418,417,413,414,415,416,688,85,84,89,87,88,86,82,81,83,79,80,78,94,93,95,92,90,91,180,182,181,184,185,183,143,142,141,139,140,138,77,76,75,74,72,73,97,96,98,101,99,100,266,265,264,267,268,269,197,196,195,192,193,194,201,203,202,198,199,200,189,191,190,186,187,188,371,370,366,367,368,369,512,511,513,509,508,510,428,427,429,430,425,426,394,393,389,390,391,392,424,423,419,420,421,422,431,436,432,433,434,435,383,388,384,385,386,387,563,562,564,565,596,591,593,597,592,595,594,566,635,648,637,636,638,616,617,624,625,618,627,690,706,666,662,676,705,661,695,680,54,56,58,59,57,55,36,38,37,39,40,41,53,52,51,48,49,50,45,47,46,43,44,42,61,60,62,63,64,65,69,71,70,66,67,68,271,270,272,275,273,274,211,210,212,215,213,214,280,279,281,278,276,277,257,256,255,254,252,253,251,250,249,248,246,247,601,600,598,599,526,527,347,346,342,343,344,345,483,482,484,479,480,481,474,473,475,476,477,478,536,537,538,539,540,541,442,441,437,438,439,440,545,544,546,573,574,575,586,585,583,584,552,553,486,485,487,488,489,568,611,640,651,645,646,615,613,610,650,612,614,704,698,667,677,682,693,683,687,681,258,260,262,263,261,259,11,10,9,8,6,7,126,128,127,130,131,129,125,124,123,120,121,122,205,204,206,207,208,209,145,144,146,148,149,147,220,219,221,218,216,217,297,299,298,295,296,294,32,31,30,33,34,35,312,314,313,315,316,317,25,24,26,28,29,27,491,495,490,492,493,494,331,335,330,332,333,334,350,349,351,352,353,348,356,355,357,358,359,354,521,525,520,522,523,524,364,363,365,360,361,362,550,549,551,582,580,581,572,571,569,570,542,543,558,557,559,560,561,590,622,654,609,608,657,628,647,660,641,623,639,691,699,696,684,671,697,692,686,663,305,304,300,301,302,303,158,157,156,161,159,160,320,319,318,321,322,323,283,282,284,287,285,286,223,222,224,225,226,227,153,155,154,150,151,152,132,134,133,136,137,135,4,3,5,2,1,0,238,237,239,236,234,235,17,16,15,12,13,14,242,241,240,245,243,244,603,602,604,605,535,534,472,471,467,468,469,470,500,499,501,497,496,498,519,518,515,514,516,517,504,502,505,506,507,503,464,463,465,466,461,462,556,555,554,589,588,587,576,579,577,578,547,548,380,379,381,382,378,567,652,606,643,644,607,630,655,631,626,658,642,689,670,669,665,664,685,694,668,678,105,107,103,104,102,106,108,110,109,111,112,113,174,176,175,178,179,177,118,117,119,116,114,115,171,173,172,170,168,169,22,21,23,19,20,18,326,325,324,327,328,329,233,232,231,228,229,230,167,166,165,162,163,164,308,307,306,311,309,310,290,289,288,293,291,292,396,395,397,398,399,400,340,339,341,336,337,338,412,411,407,408,409,410,374,373,375,376,377,372,405,404,406,401,402,403,532,531,533,529,528,530,444,443,445,446,447,448,451,450,452,453,454,449,460,459,455,456,457,458,621,649,632,653,656,629,619,620,659,634,633,672,673,703,700,701,702,674,675,679 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#141a5ad98d093a51cbcd8d0e5f762ac857a7d54b6447f4e2b6939d4d1af2e3e9, M = {102, 103, 104, 105, 106, 107, 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 16:57:28 · history