Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma b34c74d0b248…

magma b34c74d0b248
Size
707
Isomorphism class hash
b34c74d0b248e208134d564e6224eaa95d1f845eaed280b754464c4a34e85b07
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
2026-10-08 01:16:33
Display reorder
210,212,213,214,215,211,706,292,291,293,289,288,290,295,299,294,296,297,298,305,304,301,300,302,303,254,253,255,256,257,252,286,285,287,283,282,284,223,222,224,225,226,227,25,24,26,27,28,29,221,220,216,217,218,219,92,91,93,94,95,90,260,259,261,262,263,258,596,594,595,598,599,597,591,593,592,589,590,588,359,361,360,364,362,363,519,518,520,523,521,522,366,365,367,370,368,369,584,582,583,585,586,587,603,605,604,601,602,600,581,580,579,576,578,577,328,327,329,325,326,324,323,322,321,320,318,319,651,633,642,654,641,655,643,653,652,632,691,692,697,701,705,703,700,704,702,693,119,118,114,115,116,117,269,268,265,264,266,267,9,8,10,11,6,7,111,110,112,113,108,109,179,178,174,175,176,177,169,168,170,171,172,173,273,272,274,275,271,270,5,4,1,0,2,3,89,88,84,85,86,87,166,165,167,162,163,164,460,459,458,462,463,461,472,471,470,473,474,475,482,484,483,487,485,486,423,425,424,427,428,426,430,429,431,434,432,433,411,393,392,389,390,391,380,382,381,378,379,377,373,372,371,375,376,374,539,541,540,542,543,544,533,535,534,531,545,532,635,606,637,617,634,636,650,648,631,649,689,699,696,681,688,679,680,682,669,668,152,151,153,154,155,150,144,149,145,146,147,148,131,130,126,127,128,129,68,67,69,70,71,66,276,277,278,279,280,281,31,30,32,33,34,35,241,240,242,243,244,245,53,52,48,49,50,51,64,63,65,60,61,62,193,192,194,195,196,197,341,343,342,346,344,345,410,409,413,408,406,407,397,399,398,396,394,395,570,571,572,575,573,574,562,561,563,560,559,558,331,412,330,332,333,334,348,347,349,352,350,351,565,566,564,569,567,568,513,512,514,516,517,515,446,448,447,449,450,451,630,639,640,629,638,624,625,627,626,628,673,698,694,683,677,690,670,686,666,676,47,46,42,43,44,45,36,41,37,38,39,40,190,189,191,186,187,188,238,237,239,234,235,236,55,54,56,57,58,59,251,250,246,247,248,249,199,198,200,201,202,203,76,75,77,72,73,74,82,81,83,78,79,80,204,209,205,206,207,208,337,336,335,339,340,338,405,404,403,400,401,402,547,546,548,549,550,551,554,552,553,555,556,557,536,538,537,414,415,416,526,525,524,527,528,529,435,437,436,439,440,438,441,530,442,443,444,445,507,506,508,510,511,509,312,314,313,315,316,317,622,609,613,610,623,614,645,644,646,647,678,687,695,675,684,674,667,685,672,671,156,161,157,158,159,160,180,185,181,182,183,184,20,19,21,22,23,18,12,17,13,14,15,16,98,97,99,100,101,96,103,102,104,105,106,107,229,228,230,231,232,233,123,122,124,125,120,121,141,140,142,143,138,139,132,137,133,134,135,136,422,421,420,418,419,417,479,481,480,477,478,476,468,467,469,464,465,466,457,456,455,452,453,454,354,353,355,358,356,357,309,311,310,306,308,307,492,491,493,490,488,489,495,494,496,497,498,499,505,504,503,502,500,501,386,388,387,383,384,385,607,611,612,616,618,608,615,620,621,619,658,664,665,660,663,662,657,661,656,659 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#e4013d0178842fa1abe6ac84eb6d8732370ca50237187a2a953024cf339ab2c2, 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 2026-10-08 01:16:34 · history