Equation 677 Database

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Magma f01596eef179…

magma f01596eef179
Size
707
Isomorphism class hash
f01596eef17947f9fb211eb71041f9d9dca37fae15f54f87e282e75e3e0505c5
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
2026-10-06 09:37:29
Display reorder
75,74,76,77,72,73,706,278,279,280,281,277,276,92,91,93,94,95,90,291,290,292,293,289,288,11,10,6,7,8,9,302,300,303,304,305,301,189,188,190,191,186,187,286,285,287,283,282,284,86,85,87,88,89,84,79,78,80,81,82,83,298,297,299,295,294,296,437,436,435,434,432,433,531,533,532,530,528,529,525,527,526,524,522,523,604,603,605,601,600,602,516,518,517,519,520,521,443,442,441,439,440,438,335,334,333,331,332,330,338,337,336,340,341,339,342,344,343,347,345,346,595,596,594,597,598,599,653,650,643,642,651,652,654,655,635,634,703,677,697,704,702,691,701,698,705,699,109,110,111,112,113,108,129,128,130,131,126,127,123,122,124,125,120,121,2,0,3,4,5,1,150,155,151,152,153,154,270,271,272,273,274,275,163,162,164,165,166,167,116,115,117,118,119,114,182,181,183,184,185,180,171,170,172,173,168,169,487,486,488,490,491,489,500,499,498,502,503,501,505,504,506,507,508,509,327,329,328,326,324,325,417,419,418,414,415,416,375,374,373,371,372,370,352,351,353,348,349,350,355,354,356,357,358,359,362,364,363,361,360,382,384,386,385,387,388,389,637,631,639,628,638,621,633,648,646,649,700,696,694,689,673,667,679,666,690,680,146,147,148,149,144,145,139,138,140,141,142,143,196,195,197,192,193,194,62,61,63,64,65,60,203,202,198,199,200,201,246,247,248,249,250,251,56,55,57,58,59,54,20,19,21,22,23,18,264,265,266,267,268,269,221,220,216,217,218,219,564,565,566,568,569,567,570,572,571,573,574,575,308,306,307,310,311,309,581,580,579,576,578,577,461,460,459,458,456,457,593,592,591,588,590,589,447,449,448,446,444,445,546,548,547,551,549,550,563,562,561,559,560,558,585,587,586,583,582,584,625,640,612,636,613,641,626,627,629,630,693,692,686,683,668,670,672,674,681,688,17,12,13,14,15,16,245,244,241,240,242,243,226,225,227,222,223,224,235,234,236,237,238,239,50,49,51,52,53,48,230,229,231,232,233,228,215,214,210,211,212,213,26,25,27,28,29,24,158,157,159,160,161,156,209,208,204,205,206,207,452,451,450,455,453,454,462,464,463,467,465,466,397,396,398,399,400,401,392,391,390,394,395,393,542,541,540,545,543,544,318,320,319,323,321,322,405,407,406,404,402,403,314,313,312,316,317,315,535,534,536,537,538,539,554,553,552,557,555,556,609,606,610,611,608,607,632,644,647,645,695,682,685,687,671,665,675,676,684,678,132,133,134,135,136,137,102,107,103,104,105,106,31,30,32,33,34,35,41,40,36,37,38,39,46,45,47,42,43,44,254,257,253,256,255,252,258,259,260,261,262,263,178,177,179,174,175,176,98,97,99,100,101,96,69,68,70,71,66,67,423,425,424,420,421,422,412,411,413,408,409,410,368,381,369,367,365,366,473,472,471,469,470,468,494,493,492,497,495,496,482,481,480,484,485,483,478,477,479,474,475,476,514,513,515,510,511,512,376,378,377,383,379,380,430,429,431,427,428,426,617,615,614,620,618,619,622,623,616,624,669,659,663,664,656,657,660,658,661,662 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, 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 2026-10-06 09:37:30 · history