Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma d4e20c68a7e2…

magma d4e20c68a7e2
Size
595
Isomorphism class hash
d4e20c68a7e2ca2d24bed8f54ab5619cfe02a1d1cbddf5cd16afe8af323069f9
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 10:42:10
Display reorder
175,177,176,172,173,174,155,154,156,158,159,157,56,58,57,55,53,54,270,275,271,272,273,274,441,440,442,443,438,439,533,536,518,573,554,114,113,115,118,116,117,119,121,120,124,122,123,93,92,94,178,149,150,163,165,164,162,160,161,195,191,187,183,256,253,204,203,202,205,206,207,245,244,246,249,247,248,132,131,133,136,134,135,298,297,299,294,295,296,472,471,473,468,469,470,301,300,302,303,304,305,292,291,293,288,289,290,281,280,276,277,278,279,372,377,373,374,375,376,341,340,336,337,338,339,453,452,454,455,450,451,537,545,552,530,534,543,528,527,592,576,556,572,582,583,579,581,210,209,208,211,212,213,241,243,242,240,238,239,250,254,180,189,193,185,52,51,50,48,49,47,12,14,13,15,16,17,138,137,139,142,140,141,3,5,4,0,2,1,223,225,224,221,222,220,508,507,509,504,505,506,432,437,433,434,435,436,481,480,482,483,484,485,400,399,401,396,397,398,427,426,428,429,430,431,393,392,394,395,390,391,387,386,388,389,384,385,371,370,366,367,368,369,540,539,510,548,517,512,551,546,588,557,563,590,580,585,577,570,68,70,69,66,67,65,125,127,126,130,128,129,148,147,146,145,143,144,29,28,27,25,26,24,80,82,81,83,84,85,44,46,45,42,43,41,112,111,110,107,108,109,96,95,97,100,98,99,414,419,415,416,417,418,501,500,502,503,498,499,474,479,475,476,477,478,314,313,315,316,317,312,497,496,492,493,494,495,365,364,360,361,362,363,263,262,259,258,260,261,345,344,346,347,342,343,531,516,526,524,514,522,529,520,594,565,561,569,587,566,586,564,229,231,230,227,228,226,214,216,215,219,217,218,252,257,181,190,194,186,39,38,40,35,36,37,21,23,22,18,19,20,71,73,72,75,76,74,106,105,104,101,102,103,152,151,153,78,79,77,407,406,402,403,404,405,287,286,282,283,284,285,306,311,307,308,309,310,446,445,447,448,449,444,333,332,334,335,330,331,379,378,380,381,382,383,325,324,326,327,328,329,424,423,425,420,421,422,541,521,525,532,515,513,547,549,593,562,575,567,574,591,571,555,167,166,168,171,169,170,62,64,63,61,59,60,33,32,34,30,31,179,88,87,86,90,91,89,192,188,184,182,255,251,232,234,233,236,237,235,197,196,198,201,199,200,7,8,6,10,11,9,349,348,350,351,352,353,487,486,488,489,490,491,459,458,460,461,456,457,462,467,463,464,465,466,357,356,358,359,354,355,411,410,412,413,408,409,318,323,319,320,321,322,267,266,268,269,264,265,538,550,544,511,523,542,519,535,553,568,558,559,560,578,584,589 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = the submagma generated by {0, 30} (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 10:42:11 · history