Equation 677 Database

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Magma 7c049dd3a5fc…

magma 7c049dd3a5fc
Size
381
Isomorphism class hash
7c049dd3a5fcc14d8577760bdff3bfc0973f86917539f4dfd1159a2e55f00a68
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 23:21:57
Display reorder
380,55,46,36,251,231,241,310,306,308,20,31,10,115,96,100,105,0,131,141,191,170,176,186,80,90,70,200,211,221,155,255,166,145,271,150,276,160,51,41,290,236,309,307,5,15,110,125,136,196,75,85,226,206,260,265,60,246,311,26,120,281,181,66,216,285,296,340,333,370,379,349,339,350,359,369,362,58,48,38,254,234,244,327,329,325,23,33,14,118,98,104,108,4,133,143,194,174,179,189,83,93,74,204,214,224,158,259,169,149,273,154,278,163,53,44,294,239,326,324,8,18,113,128,138,199,78,88,229,209,264,268,63,249,328,28,123,283,184,68,219,289,299,343,334,373,375,345,335,354,355,367,361,57,47,37,253,233,243,304,301,302,22,32,12,117,97,102,107,2,132,142,193,173,178,188,82,92,72,203,213,223,157,257,167,147,272,152,277,162,52,42,293,238,303,300,7,17,112,127,137,198,77,87,228,208,262,267,62,248,305,27,122,282,183,67,218,287,297,342,331,371,377,347,337,352,357,368,363,59,49,39,250,230,240,322,318,320,24,34,13,119,99,103,109,3,134,144,190,171,175,185,84,94,73,201,210,220,159,258,168,148,274,153,279,164,54,43,291,235,321,319,9,19,114,129,139,195,79,89,225,205,263,269,64,245,323,29,124,284,180,69,215,288,298,344,332,374,378,348,338,353,358,365,364,56,45,35,252,232,242,313,315,317,21,30,11,116,95,101,106,1,130,140,192,172,177,187,81,91,71,202,212,222,156,256,165,146,270,151,275,161,50,40,292,237,312,316,6,16,111,126,135,197,76,86,227,207,261,266,61,247,314,25,121,280,182,65,217,286,295,341,330,372,376,346,336,351,356,366,360 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {69} 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 23:21:58 · history