Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma f80728aa22db…

magma f80728aa22db
Size
595
Isomorphism class hash
f80728aa22db774c3f3427e542fdfda418aa1480b0fe4baa35cef544ea4c1a84
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 18:51:43
Display reorder
508,505,509,506,507,504,442,441,443,438,439,440,427,431,426,428,429,430,434,433,435,436,437,432,274,273,275,270,272,271,555,591,592,594,593,399,398,400,401,396,397,395,394,390,391,392,393,496,495,497,492,493,494,491,490,486,487,488,489,385,384,386,387,388,389,402,407,403,404,405,406,383,382,378,379,380,381,248,247,246,250,251,249,199,198,197,202,200,201,252,254,253,257,255,256,111,113,112,110,108,109,10,9,11,8,6,7,177,176,175,173,174,172,1,2,0,5,3,4,118,117,119,116,114,115,120,122,121,125,123,124,541,538,522,532,548,526,510,551,516,576,582,586,562,571,566,557,423,422,424,425,420,421,419,418,414,415,416,417,450,455,451,452,453,454,503,502,498,499,500,501,409,408,410,411,412,413,282,287,283,284,285,286,281,280,277,276,278,279,260,259,258,262,263,261,205,204,203,208,206,207,217,216,218,219,220,221,129,131,130,128,126,127,20,19,18,21,22,23,158,160,159,157,155,156,24,26,25,29,27,28,149,148,147,144,145,146,31,30,32,33,34,35,544,535,524,533,549,529,514,554,519,580,585,590,565,575,570,560,373,372,374,375,376,377,369,368,370,371,366,367,484,483,485,480,481,482,476,475,477,478,479,474,365,364,360,361,362,363,349,348,350,351,352,353,354,359,355,356,357,358,235,234,236,237,238,239,182,184,183,181,209,180,240,242,241,245,243,244,95,94,93,91,92,90,88,87,89,86,84,85,171,170,169,167,168,166,83,82,81,79,80,78,99,101,100,97,98,96,102,104,103,107,105,106,542,537,521,531,547,527,512,552,517,578,583,588,563,572,569,558,327,326,328,329,324,325,331,330,332,333,334,335,468,473,469,470,471,472,466,465,467,462,463,464,319,318,320,321,322,323,336,341,337,338,339,340,347,346,342,343,344,345,230,229,228,232,233,231,194,196,195,191,192,193,265,266,264,269,267,268,63,65,64,62,60,61,66,68,67,70,71,69,164,163,165,161,179,162,134,132,133,136,137,135,143,142,141,139,138,140,74,73,72,76,77,75,543,539,523,534,546,528,513,553,518,579,584,589,564,574,568,559,316,315,317,312,313,314,306,311,307,308,309,310,449,448,444,445,446,447,460,459,461,456,457,458,301,300,302,303,304,305,293,292,288,289,290,291,298,297,299,294,295,296,226,225,227,222,223,224,187,186,185,190,188,189,213,215,214,212,211,210,51,53,52,50,48,49,45,47,46,43,44,42,151,150,178,152,153,154,40,39,41,36,37,38,54,56,55,58,59,57,17,16,15,13,14,12,540,536,520,530,545,525,511,550,515,577,581,587,561,573,567,556 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = the submagma generated by {0, 6} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 18:51:44 · history