Equation 677 Database

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Magma a23ba5509217…

magma a23ba5509217
Size
707
Isomorphism class hash
a23ba55092173f9bd027da45ac21dc59d1b23e11f37c289a08998e76dc0f6d0a
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 10:48:08
Display reorder
554,553,552,550,551,549,628,134,133,135,136,137,132,103,104,105,106,107,102,118,117,119,114,115,116,99,98,100,101,96,97,10,9,11,6,7,8,206,205,207,208,209,204,85,84,86,87,88,89,32,31,33,34,35,30,249,248,250,251,247,246,77,76,72,73,74,75,301,305,300,302,303,304,382,381,380,385,383,384,407,409,408,412,410,411,437,439,438,442,440,441,466,465,464,462,463,461,334,333,335,337,338,336,474,473,472,476,477,475,363,362,364,365,366,367,592,591,593,594,595,596,589,588,590,598,360,361,617,643,613,615,614,616,623,645,647,699,665,678,700,683,698,697,687,702,705,706,70,69,71,66,67,68,42,43,44,45,46,47,78,83,79,80,81,82,55,54,56,57,58,59,202,201,203,198,199,200,37,36,38,39,40,41,297,296,298,299,294,295,289,288,290,291,292,293,126,131,127,128,129,130,50,49,51,52,53,48,60,65,61,62,63,64,435,434,436,432,433,431,355,354,356,357,358,359,576,577,578,579,580,581,430,429,428,426,427,425,420,419,421,423,424,422,443,445,444,448,446,447,480,479,478,482,483,481,353,352,351,349,350,348,415,414,413,418,416,417,637,624,607,606,649,648,625,642,626,675,681,695,679,657,667,674,666,676,686,696,266,265,267,268,269,264,113,108,109,110,111,112,26,25,27,28,29,24,285,284,286,287,282,283,168,173,169,170,171,172,263,262,258,259,260,261,2,0,3,4,5,1,151,155,152,154,150,153,141,140,142,143,138,139,279,278,280,281,276,277,147,146,148,149,144,145,560,559,558,557,555,556,486,485,484,488,489,487,341,340,339,330,332,331,394,393,392,396,397,395,451,450,449,454,452,453,605,604,603,601,602,600,504,503,502,506,507,505,540,542,541,539,537,538,547,546,548,544,545,543,627,646,619,644,611,618,609,612,620,694,680,688,691,660,668,685,662,692,677,701,161,160,156,157,158,159,221,216,217,218,219,220,182,181,183,184,185,180,308,307,309,310,311,306,241,240,242,243,244,245,313,312,314,315,316,317,255,254,256,257,252,253,235,234,236,237,238,239,274,273,275,270,271,272,233,232,228,229,230,231,179,178,174,175,176,177,400,399,398,403,401,402,344,343,342,346,347,345,460,459,458,456,457,455,514,516,515,519,517,518,528,530,529,525,526,527,567,568,569,570,571,572,565,564,566,562,561,563,492,491,490,494,495,493,498,497,496,501,499,500,639,621,622,608,638,610,640,651,650,703,671,684,704,664,672,682,663,689,690,693,164,163,165,166,167,162,193,194,195,196,197,192,215,214,210,211,212,213,223,222,224,225,226,227,326,328,327,324,325,329,13,12,14,15,16,17,124,123,125,120,121,122,323,322,319,318,320,321,188,187,189,190,191,186,18,23,19,20,21,22,91,90,92,93,94,95,532,531,533,535,536,534,470,469,471,467,468,599,584,583,582,586,587,585,369,368,370,371,372,373,520,597,521,523,524,522,573,575,574,406,404,405,510,509,508,512,513,511,375,374,376,377,378,379,386,388,387,389,390,391,641,632,631,629,636,633,635,630,634,670,656,661,669,653,654,655,652,659,658,673 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 = {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 2026-10-06 10:48:09 · history