Equation 677 Database

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Magma b7befc4c1dda…

magma b7befc4c1dda
Size
381
Isomorphism class hash
b7befc4c1dda3563bd1f7ab0201f14d2d24ed98a507b0feba4fa8a6d93e217ed
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:51:19
Display reorder
380,18,13,23,3,8,267,97,92,282,88,77,83,48,43,273,38,28,33,318,319,320,321,322,323,185,175,180,200,191,196,211,216,206,225,230,220,108,113,102,285,120,117,247,238,243,263,253,258,67,72,62,52,57,277,137,126,131,145,140,291,296,155,150,171,160,166,366,370,342,355,347,352,337,333,360,376,17,12,22,2,5,268,98,93,283,86,78,81,46,41,270,35,26,30,329,327,328,326,324,325,187,177,182,202,192,197,212,217,207,227,232,222,106,110,103,288,123,118,248,236,241,261,251,256,68,73,63,53,58,278,135,127,130,147,142,292,297,157,152,172,162,167,367,372,343,358,348,353,338,331,362,377,19,14,24,4,7,269,99,94,284,89,79,84,49,44,274,39,29,34,306,307,308,309,310,311,188,178,183,203,193,198,213,218,208,228,233,223,109,114,104,289,124,119,249,239,244,264,254,259,69,74,64,54,59,279,138,128,133,148,143,293,298,158,153,173,163,168,368,373,344,359,349,354,339,334,364,378,16,10,20,1,9,266,96,91,280,85,76,80,47,42,272,37,27,32,316,317,315,313,314,312,186,176,181,201,190,195,210,215,205,226,231,221,105,111,100,287,122,115,246,237,240,262,252,257,66,70,61,51,56,275,136,125,132,146,141,290,295,156,151,170,161,165,365,371,340,357,345,350,336,332,361,375,15,11,21,0,6,265,95,90,281,87,75,82,45,40,271,36,25,31,300,302,301,304,305,303,189,179,184,204,194,199,214,219,209,229,234,224,107,112,101,286,121,116,245,235,242,260,250,255,65,71,60,50,55,276,139,129,134,149,144,294,299,159,154,174,164,169,369,374,341,356,346,351,335,330,363,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {75} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:51:20 · history