Equation 677 Database

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Magma 1f32d56260d8…

magma 1f32d56260d8
Size
381
Isomorphism class hash
1f32d56260d882efcf922d53785eb1351fb8fe9631683b8c6f2bc035092fa790
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 23:37:46
Display reorder
380,296,281,275,266,272,261,191,196,201,207,212,217,328,329,327,325,326,324,250,46,41,30,35,25,237,242,247,224,229,232,95,256,90,81,86,75,100,105,110,115,120,125,141,131,136,156,146,151,176,181,186,160,165,170,290,70,66,55,60,50,11,10,12,287,8,9,335,346,356,376,351,340,364,365,331,370,298,283,278,268,273,263,193,198,203,208,213,218,303,304,305,301,300,302,253,48,43,33,38,28,238,243,248,220,225,233,98,258,93,83,88,78,103,108,112,118,123,128,143,133,138,158,148,153,178,183,188,163,168,173,293,73,68,58,63,53,16,15,17,288,18,19,338,348,358,378,353,342,362,368,333,373,295,280,276,267,271,262,190,195,200,205,210,215,320,318,319,323,321,322,251,45,40,31,36,26,236,241,245,222,227,230,96,255,91,80,85,76,102,106,114,116,121,126,140,130,135,155,145,150,175,180,185,161,166,171,291,71,65,56,61,51,3,13,4,285,5,6,336,345,355,375,350,341,360,366,330,371,299,284,279,269,274,264,194,199,204,209,214,219,308,306,307,311,309,310,254,49,44,34,39,29,239,244,249,221,226,234,99,259,94,84,89,79,104,109,113,119,124,129,144,134,139,159,149,154,179,184,189,164,169,174,294,74,69,59,64,54,21,20,22,289,23,24,339,349,359,379,354,344,363,369,334,374,297,282,277,265,270,260,192,197,202,206,211,216,316,317,315,313,314,312,252,47,42,32,37,27,235,240,246,223,228,231,97,257,92,82,87,77,101,107,111,117,122,127,142,132,137,157,147,152,177,182,187,162,167,172,292,72,67,57,62,52,1,2,0,286,7,14,337,347,357,377,352,343,361,367,332,372 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, 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 23:37:47 · history