Equation 677 Database

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Magma 6c2d4921a6d7…

magma 6c2d4921a6d7
Size
381
Isomorphism class hash
6c2d4921a6d7d36447cc4dfbdd3c233265e3d6f57a9ebb10deb73c244ff5fd7d
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 23:47:29
Display reorder
380,113,283,118,108,98,36,40,20,266,25,182,186,176,195,201,103,31,190,239,242,245,251,255,260,93,83,88,78,73,278,8,9,295,161,166,172,311,309,310,308,306,307,56,46,51,272,60,67,155,151,290,147,135,140,221,226,231,205,210,215,126,121,131,1,0,286,365,356,353,330,336,342,360,371,348,375,112,282,117,107,97,38,43,23,268,28,183,187,178,198,203,102,33,193,237,241,246,252,257,262,92,82,87,77,72,277,14,15,298,163,168,174,315,316,317,312,313,314,58,48,53,273,63,68,158,153,293,148,138,143,222,227,232,207,212,217,128,123,133,13,12,288,368,358,352,331,338,343,363,372,347,377,110,281,115,106,96,35,41,21,265,26,181,185,177,197,202,101,30,192,235,243,247,253,258,263,90,80,85,76,71,275,10,11,297,162,167,173,318,319,320,321,322,323,57,45,52,270,62,66,157,152,292,145,137,142,220,225,230,206,211,216,125,120,132,6,7,287,367,357,351,332,335,340,362,370,345,376,111,280,116,105,95,37,42,22,267,27,180,188,175,196,200,100,32,191,238,244,248,250,256,261,91,81,86,75,70,276,2,3,296,160,165,171,326,324,325,329,327,328,55,47,50,271,61,65,156,150,291,146,136,141,223,228,233,208,213,218,127,122,130,4,5,285,366,355,350,333,337,341,361,373,346,378,114,284,119,109,99,39,44,24,269,29,184,189,179,199,204,104,34,194,236,240,249,254,259,264,94,84,89,79,74,279,18,19,299,164,169,170,302,301,300,305,303,304,59,49,54,274,64,69,159,154,294,149,139,144,224,229,234,209,214,219,129,124,134,17,16,289,369,359,354,334,339,344,364,374,349,379 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, 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 23:47:30 · history