Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma def872c79226…

magma def872c79226
Size
707
Isomorphism class hash
def872c79226ed53a4745dc88902822aa67b28f631999e2b07e0c747b238eb51
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 06:26:00
Display reorder
104,103,105,106,107,102,706,151,154,152,153,150,155,120,125,121,122,123,124,22,21,23,18,19,20,88,87,89,84,85,86,209,208,205,204,206,207,140,139,141,142,143,138,17,16,12,13,14,15,288,289,290,291,292,293,298,297,299,295,294,296,304,305,301,302,303,300,404,403,402,405,406,407,411,413,412,408,409,410,434,433,432,435,436,437,371,370,369,366,367,368,345,347,346,344,342,343,575,574,573,572,571,570,461,460,459,458,456,457,449,448,447,446,444,445,357,359,358,356,354,355,318,320,319,321,322,323,616,615,613,614,611,612,642,640,641,631,695,696,672,690,704,700,701,699,705,697,226,223,227,222,225,224,215,214,210,211,212,213,37,36,38,39,40,41,61,60,62,63,64,65,129,128,130,131,126,127,49,48,50,51,52,53,231,230,232,233,229,228,193,192,194,195,196,197,32,31,33,34,35,30,26,25,27,28,29,24,377,376,375,372,373,374,390,392,391,393,394,395,308,306,307,309,310,311,502,501,503,500,498,499,398,397,396,400,401,399,521,520,519,518,516,517,417,419,418,414,415,416,478,477,479,475,476,474,497,496,495,493,494,492,508,507,509,505,506,504,623,608,625,610,607,624,636,630,637,622,694,702,675,666,689,685,684,671,683,674,68,71,69,70,67,66,75,74,76,77,72,73,183,182,184,185,180,181,201,200,202,203,198,199,116,115,117,118,119,114,55,54,56,57,58,59,241,240,242,243,244,245,246,251,247,248,249,250,269,268,265,264,266,267,136,135,137,132,133,134,466,465,467,464,462,463,328,327,329,325,326,324,382,381,383,380,378,379,388,387,389,386,384,385,565,566,564,569,567,568,553,552,554,556,557,555,563,562,561,560,558,559,353,352,351,350,348,349,544,543,545,540,541,542,515,514,513,512,510,511,617,644,618,645,621,646,606,609,619,620,686,703,668,667,679,693,677,680,681,676,177,174,178,179,176,175,235,234,236,237,238,239,190,189,191,186,187,188,284,282,285,286,287,283,274,273,275,271,270,272,164,163,165,166,167,162,216,221,217,218,219,220,47,46,42,43,44,45,173,172,168,169,170,171,278,276,279,280,281,277,313,312,314,317,315,316,596,594,595,598,597,599,489,491,490,487,488,486,526,525,527,524,522,523,601,602,600,605,603,604,331,330,332,334,335,333,582,583,584,586,587,585,590,588,589,593,591,592,481,480,482,483,484,485,576,577,578,580,581,579,651,647,643,639,649,650,648,653,638,654,691,698,665,664,688,692,678,682,687,673,3,1,4,5,2,0,156,161,157,158,159,160,98,97,99,100,101,96,260,258,261,262,263,259,109,108,110,111,112,113,11,10,6,7,8,9,93,92,94,95,90,91,144,149,145,146,147,148,252,253,254,255,256,257,81,80,82,83,78,79,473,472,471,468,469,470,424,423,425,421,422,420,531,533,532,529,530,528,454,453,455,452,450,451,441,443,442,440,438,439,535,534,536,538,539,537,551,550,549,548,546,547,429,431,430,426,427,428,337,336,338,339,340,341,362,361,360,365,363,364,629,633,628,652,626,632,627,634,635,655,660,670,656,657,661,669,663,658,662,659 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#d668bf04c36f8b4c67728650c5c82a046d470936a3c130394e60cdea0aa42f4e, M = {42, 43, 44, 45, 46, 47, 140} 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 06:26:01 · history