Equation 677 Database

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Magma 9db925679ca2…

magma 9db925679ca2
Size
707
Isomorphism class hash
9db925679ca20c4097b32ec2e6a7546de798e7ee532743c31f52fa957d5ae676
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 20:43:40
Display reorder
182,181,183,184,185,180,706,37,38,39,40,41,36,99,98,100,101,96,97,145,144,146,147,148,149,134,133,135,136,137,132,278,276,279,280,281,277,15,14,16,17,12,13,320,319,321,322,323,318,56,55,57,58,59,54,270,275,271,272,273,274,333,332,334,335,331,330,326,325,324,327,328,329,407,406,405,404,402,403,537,539,538,536,534,535,343,342,344,347,345,346,373,372,374,376,377,375,385,384,386,388,389,387,363,365,364,360,361,362,435,437,436,432,433,434,527,526,525,522,523,524,393,395,394,391,392,390,611,609,610,607,606,608,637,635,639,694,667,656,673,701,703,699,698,705,704,700,26,24,29,27,28,25,84,89,85,86,87,88,124,123,125,120,121,122,157,156,158,159,160,161,262,261,263,258,259,260,61,60,62,63,64,65,222,227,223,224,225,226,288,289,290,291,292,293,239,238,234,235,236,237,232,231,233,228,229,230,294,295,296,297,298,299,549,551,550,547,546,548,471,470,472,467,468,469,462,461,463,466,464,465,574,573,575,570,572,571,456,485,457,459,460,458,484,483,482,481,479,480,474,473,475,477,478,476,521,520,519,516,517,518,578,576,577,579,580,581,622,613,612,624,614,615,630,634,633,675,674,665,660,685,687,676,688,695,684,686,242,243,244,245,240,241,113,112,108,109,110,111,208,207,209,204,205,206,48,53,49,50,51,52,2,0,3,4,5,1,214,213,215,210,211,212,115,114,116,117,118,119,253,252,254,255,256,257,93,92,94,95,90,91,313,317,312,314,315,316,70,69,71,66,67,68,552,554,553,555,557,556,567,569,568,566,564,565,358,357,359,356,354,355,513,515,514,510,511,512,509,508,507,506,504,505,501,503,502,498,499,500,496,495,497,493,494,492,561,563,562,558,560,559,584,582,583,585,586,587,627,631,625,626,628,629,638,632,636,679,669,662,663,690,680,689,677,702,670,683,264,265,266,267,268,269,218,217,219,220,221,216,193,192,194,195,196,197,77,76,72,73,74,75,172,171,173,168,169,170,178,177,179,174,175,176,203,202,198,199,200,201,126,131,127,128,129,130,34,33,35,30,31,32,167,166,162,163,164,165,80,79,81,82,83,78,588,589,590,592,593,591,431,430,429,427,428,426,414,416,415,418,419,417,421,420,422,424,425,423,604,603,605,600,602,601,454,453,455,451,452,450,595,596,594,597,598,599,486,488,487,490,491,489,533,532,531,528,529,530,646,644,642,643,640,641,645,648,647,697,664,657,691,692,693,682,672,696,681,678,283,284,285,286,287,282,309,308,310,311,307,306,248,247,249,250,251,246,7,6,8,9,10,11,300,305,303,301,302,304,189,188,190,191,186,187,155,154,150,151,152,153,19,18,20,21,22,23,102,107,103,104,105,106,138,143,139,140,141,142,42,47,43,44,45,46,351,353,352,348,349,350,381,383,382,380,378,379,438,440,439,442,443,441,340,339,341,336,338,337,371,370,369,368,366,367,400,399,401,397,398,396,541,540,542,544,545,543,446,445,444,447,448,449,410,409,408,411,412,413,617,618,620,621,616,619,623,650,649,668,653,651,652,666,659,658,661,671,655,654 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {18, 19, 20, 21, 22, 23, 143} 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 20:43:44 · history