Equation 677 Database

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Magma d8e9f8fe8323…

magma d8e9f8fe8323
Size
707
Isomorphism class hash
d8e9f8fe83233c91f45653983eef095386f3713eabae6fb144fe560562d2856c
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 19:08:01
Display reorder
298,297,299,295,294,296,656,185,184,183,182,181,180,222,221,223,226,224,225,248,250,249,245,246,247,93,92,94,89,90,91,231,230,232,228,229,227,186,187,188,189,190,191,107,109,108,110,111,112,32,34,33,30,31,29,161,160,159,156,157,158,98,100,99,96,97,95,524,523,525,526,521,522,380,379,381,382,383,378,332,331,333,334,335,330,476,475,477,478,473,474,418,417,419,414,415,416,351,350,352,353,348,349,358,357,359,354,355,356,560,559,561,562,557,558,566,565,567,568,563,564,427,426,428,429,430,575,635,616,610,617,627,621,620,611,632,639,667,672,677,673,685,665,690,660,686,658,38,40,39,35,36,37,238,237,236,234,233,235,192,194,193,195,196,197,75,74,76,71,72,73,65,67,66,68,69,70,21,20,22,17,18,19,169,168,170,172,173,171,83,84,85,88,86,87,241,240,239,242,243,244,204,206,205,208,209,207,394,393,395,390,391,392,320,319,321,322,323,318,468,467,469,470,471,472,493,492,494,495,496,491,403,402,404,405,406,407,479,484,480,481,482,483,366,371,367,368,369,370,534,533,535,536,537,538,441,440,442,437,438,439,450,449,451,452,453,454,652,642,634,645,651,641,619,607,626,640,693,694,695,675,669,674,680,657,661,670,259,258,257,262,260,261,149,4,3,1,0,2,26,28,27,23,24,25,252,251,253,256,254,255,42,41,43,45,46,44,150,152,151,155,153,154,61,60,59,64,62,63,165,167,166,163,164,162,145,143,144,146,147,148,77,79,78,81,82,80,431,436,432,433,434,435,460,459,455,456,457,458,411,410,412,413,408,409,310,309,311,307,306,308,372,377,373,374,375,376,325,324,326,327,328,329,344,343,345,346,347,342,314,313,315,316,317,312,553,552,554,555,556,551,550,549,545,546,547,548,650,644,629,647,655,648,614,612,630,631,692,696,691,666,678,659,679,662,668,676,106,105,104,103,101,102,9,8,10,7,5,6,174,176,175,177,178,179,198,200,199,203,201,202,12,11,13,15,16,14,56,58,57,55,53,54,47,49,48,50,51,52,140,142,141,137,139,138,215,214,213,210,211,212,263,220,219,216,217,218,361,360,362,363,364,365,401,400,396,397,398,399,338,337,339,340,341,336,466,465,461,462,463,464,544,543,539,540,541,542,445,444,446,447,448,443,425,424,420,421,422,423,573,572,574,569,570,571,486,485,487,488,489,490,532,531,527,528,529,530,654,643,633,649,653,646,615,608,637,636,682,681,671,663,683,689,664,688,684,687,304,303,305,300,302,301,293,292,291,289,288,290,266,265,264,269,267,268,117,116,118,113,114,115,122,124,123,119,120,121,277,276,278,279,280,281,275,274,273,272,270,271,130,129,128,125,126,127,135,134,136,133,131,132,285,287,286,283,284,282,514,513,509,510,511,512,581,580,576,577,578,579,520,519,515,516,517,518,604,603,605,600,601,602,500,499,501,502,497,498,508,507,503,504,505,506,590,589,591,592,593,588,385,384,386,387,388,389,597,596,598,599,594,595,584,583,585,586,587,582,638,624,609,622,628,618,613,606,625,623,699,706,698,701,697,703,704,705,700,702 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = {12, 13, 14, 15, 16, 17, 135} 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 19:08:03 · history