Equation 677 Database

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Magma ee5db31af1f4…

magma ee5db31af1f4
Size
399
Isomorphism class hash
ee5db31af1f4f6158f1785c2cf5fe0657d54598d5951ad53525d89df0b20b301
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 17:02:36
Display reorder
122,123,124,125,117,118,119,120,121,115,116,108,109,110,111,112,113,114,381,92,205,73,55,74,93,206,56,75,94,198,57,95,76,199,58,96,77,200,59,97,78,201,60,98,79,202,61,90,80,203,62,72,91,204,54,82,214,101,64,83,215,102,65,84,207,103,66,85,208,104,67,86,209,105,68,87,210,106,69,88,211,107,70,89,212,99,71,213,81,100,63,392,386,385,391,164,221,298,333,299,165,222,334,300,166,223,335,167,301,224,336,168,302,216,337,169,303,217,338,170,304,218,339,162,305,219,340,297,163,220,341,291,230,173,326,292,231,174,327,293,232,175,328,294,233,176,329,295,225,177,330,296,226,178,331,288,227,179,332,289,228,171,324,229,290,172,325,384,390,389,383,189,41,237,306,238,190,42,307,239,191,43,308,192,240,44,309,193,241,36,310,194,242,37,311,195,234,38,312,196,235,39,313,236,197,40,314,246,50,182,315,247,51,183,316,248,52,184,317,249,53,185,318,250,45,186,319,251,46,187,320,243,47,188,321,244,48,180,322,49,245,181,323,387,398,397,388,270,349,148,342,149,271,351,344,150,272,353,346,273,151,355,348,274,152,357,350,275,144,359,352,276,145,343,354,277,146,345,356,147,278,347,358,157,367,279,360,158,369,280,362,159,371,281,364,160,373,282,366,161,375,283,368,153,376,284,370,154,361,285,372,155,363,286,374,365,156,287,377,393,395,396,394,0,263,18,127,19,2,264,128,20,3,265,129,4,21,266,130,5,22,267,131,6,23,268,132,7,24,269,133,8,25,261,134,26,1,262,126,27,256,10,136,28,257,11,137,29,258,12,138,30,259,13,139,31,260,14,140,32,252,15,141,33,253,16,142,34,254,17,143,255,35,9,135,379,382,378,380 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#4fc531f265dd19d0f9a1b911ca383526db6ebaa6059d72b7bbdc277916051166, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); 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: 21.

last edited by qawbecrdtey at 2026-10-07 17:02:37 · history