Equation 677 Database

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Magma 9ccf2361a501…

magma 9ccf2361a501
Size
381
Isomorphism class hash
9ccf2361a5010da85089b7ba2a7842f8b350eb402efe995b4bdb2d02a07c9c7d
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 23:46:15
Display reorder
380,286,271,33,34,35,255,241,246,250,260,280,295,319,320,321,322,323,318,22,23,24,19,20,21,206,180,186,191,196,201,146,151,155,160,165,141,226,231,236,210,216,221,16,17,18,13,14,15,3,4,5,6,0,2,9,10,11,12,7,8,171,291,135,266,276,175,341,340,357,335,373,345,375,366,360,354,285,270,31,32,1,256,244,248,253,263,284,299,328,329,324,325,326,327,49,50,51,52,53,48,208,183,188,194,198,203,149,153,158,163,169,144,228,233,238,213,218,224,42,43,44,45,46,47,28,29,30,25,26,27,36,37,38,39,40,41,174,294,139,268,279,179,333,339,356,330,371,348,378,365,363,351,287,272,78,79,80,257,240,245,251,261,281,296,300,302,303,304,305,301,68,69,70,71,66,67,205,181,185,190,195,200,145,150,156,161,166,140,225,230,235,211,215,220,64,65,60,61,62,63,77,72,73,74,75,76,55,56,57,58,59,54,170,290,136,265,275,176,343,334,359,342,370,346,376,367,361,350,288,273,87,88,89,258,243,249,254,264,283,298,311,306,307,308,309,310,103,104,105,106,107,102,209,184,189,193,199,204,148,154,159,164,168,143,229,234,239,214,219,223,96,97,98,99,100,101,82,83,84,85,86,81,90,91,92,93,94,95,173,293,138,269,278,178,332,331,355,337,372,349,379,368,364,352,289,274,122,120,121,259,242,247,252,262,282,297,314,315,316,317,312,313,111,112,113,108,109,110,207,182,187,192,197,202,147,152,157,162,167,142,227,232,237,212,217,222,132,133,134,129,130,131,114,115,116,117,118,119,125,126,127,128,123,124,172,292,137,267,277,177,336,344,358,338,374,347,377,369,362,353 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {70} 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 23:46:15 · history