Equation 677 Database

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Magma 720b207ca7f9…

magma 720b207ca7f9
Size
707
Isomorphism class hash
720b207ca7f982b323c47497c7cecfb01393e7d072bacf1ec7292b4ce0a5a40c
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 07:41:47
Display reorder
414,413,415,416,417,418,669,146,145,148,149,147,144,134,133,132,135,136,137,158,157,156,160,161,159,162,164,163,165,166,167,140,139,138,143,141,142,130,129,131,127,128,126,87,89,88,85,86,84,169,168,170,172,173,171,50,49,48,52,53,51,154,153,155,152,150,151,121,120,122,124,125,123,371,376,372,373,374,375,426,425,427,428,429,430,447,446,448,443,444,445,440,439,441,442,437,438,433,432,434,435,436,431,366,365,367,368,369,370,423,422,424,419,420,421,563,562,564,565,596,591,593,597,592,595,594,566,628,626,639,625,638,629,623,627,624,609,617,705,704,672,666,706,674,661,673,662,65,64,60,62,61,63,18,20,19,22,23,21,10,9,11,6,7,8,284,283,282,287,285,286,231,233,232,228,229,230,83,82,81,80,78,79,73,72,74,77,75,76,16,15,17,13,14,12,297,299,298,296,295,294,222,224,223,226,227,225,93,95,94,90,91,92,603,602,604,605,518,519,403,402,404,405,406,401,449,454,450,451,452,453,504,508,503,505,506,507,458,457,459,460,455,456,481,480,482,483,484,479,543,542,544,583,581,582,574,577,575,576,537,538,356,355,357,358,354,567,651,641,618,642,613,614,616,636,660,653,654,701,697,686,676,675,687,693,688,671,98,97,100,101,99,96,46,45,47,44,42,43,30,32,31,35,33,34,312,314,313,315,316,317,326,325,324,329,327,328,320,319,318,323,321,322,247,246,248,251,249,250,116,115,114,119,117,118,272,271,270,274,275,273,195,197,196,193,194,192,179,178,177,176,174,175,492,491,493,494,495,496,523,522,524,525,521,520,407,412,408,409,410,411,549,553,548,550,551,552,360,359,361,362,363,364,557,561,556,558,559,560,540,539,541,578,579,580,570,569,571,572,516,517,513,512,514,515,511,568,657,633,630,659,619,622,658,606,608,649,645,703,699,677,698,700,685,692,696,695,185,184,181,182,180,183,262,261,263,260,258,259,102,104,103,107,105,106,201,203,202,198,199,200,256,255,257,253,254,252,277,276,278,280,281,279,28,27,29,26,24,25,292,291,293,289,290,288,4,3,5,1,0,2,210,211,212,215,213,214,237,239,238,234,235,236,598,601,599,600,509,510,500,499,501,502,497,498,463,462,464,465,466,461,534,533,535,536,532,531,393,392,394,389,390,391,384,383,385,386,387,388,546,545,547,586,584,585,589,588,590,587,554,555,527,526,528,529,530,573,634,637,643,646,631,652,650,620,647,611,610,702,691,670,667,690,668,694,664,689,69,71,68,66,67,70,59,58,57,54,55,56,302,301,300,304,305,303,310,309,311,307,308,306,221,220,219,218,216,217,40,39,41,37,38,36,264,266,265,268,269,267,245,244,243,242,240,241,189,191,190,188,186,187,112,111,113,110,108,109,204,206,205,207,208,209,485,490,486,487,488,489,471,470,472,467,468,469,353,352,348,349,350,351,334,333,335,331,330,332,341,340,336,337,338,339,342,347,343,344,345,346,378,377,379,380,381,382,399,398,400,395,396,397,477,476,478,473,474,475,656,621,635,640,615,644,607,655,612,632,648,665,679,663,683,678,684,682,680,681 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = {72, 73, 74, 75, 76, 77, 144} 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 07:41:49 · history