Equation 677 Database

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Magma 0b7b69adf221…

magma 0b7b69adf221
Size
381
Isomorphism class hash
0b7b69adf221c536b95f87bc62e8aa36d53c9e68025ea34419bb6b15b8d5db78
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 23:20:27
Display reorder
380,211,161,261,11,61,111,212,262,12,62,112,162,294,44,94,144,194,249,180,230,280,31,81,130,218,268,18,68,118,168,199,244,299,49,99,149,269,19,69,119,169,219,160,210,260,10,60,110,36,86,136,185,236,286,263,13,63,113,163,213,312,313,314,315,316,317,376,348,360,344,365,341,343,373,349,342,207,157,257,7,57,107,216,266,16,66,116,166,291,41,91,140,190,246,181,231,281,30,80,131,221,271,21,71,121,171,195,240,295,46,96,145,270,20,70,120,170,220,156,206,256,6,56,106,35,85,135,186,235,285,267,17,67,117,167,217,300,302,303,304,305,301,378,350,362,347,366,339,359,374,351,338,222,172,272,22,72,122,204,254,4,54,104,154,293,43,93,143,193,248,182,232,282,32,82,132,229,279,29,79,129,179,198,243,298,48,98,148,278,28,78,128,178,228,173,223,273,23,73,123,37,87,137,187,237,287,255,5,55,105,155,205,328,329,324,325,326,327,377,357,363,337,367,352,336,372,358,353,214,164,264,14,64,114,202,252,2,52,102,152,290,40,90,141,191,245,183,234,284,34,84,134,209,259,9,59,109,159,196,241,296,45,95,146,258,8,58,108,158,208,165,215,265,15,65,115,39,89,139,189,239,289,253,3,53,103,153,203,311,306,307,308,309,310,379,340,364,335,369,345,334,371,330,346,227,177,277,27,77,127,225,275,25,75,125,175,292,42,92,142,192,247,184,233,283,33,83,133,201,251,0,51,101,151,197,242,297,47,97,147,250,1,50,100,150,200,176,226,276,26,76,126,38,88,138,188,238,288,274,24,74,124,174,224,319,320,321,322,323,318,375,333,361,331,368,356,354,370,332,355 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {66} 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 23:20:28 · history