Equation 677 Database

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Magma 03a20b580749…

magma 03a20b580749
Size
381
Isomorphism class hash
03a20b5807492ac3ba9552069b09331aef36a27476fceb8203fe258b2d1babdf
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 23:47:25
Display reorder
380,70,65,286,50,56,206,210,185,190,195,132,137,127,147,152,61,201,142,86,91,95,290,76,81,319,320,318,322,323,321,247,252,257,262,267,272,226,216,221,240,230,235,175,181,170,160,166,156,31,36,25,281,45,40,21,11,19,5,276,0,112,107,102,297,122,117,332,357,346,350,376,370,341,336,360,367,72,67,287,52,57,207,212,187,192,197,131,136,125,145,151,62,202,140,87,92,97,292,77,82,312,313,314,315,316,317,245,250,255,261,266,271,227,217,222,242,232,237,177,182,172,162,167,157,32,37,27,282,47,42,22,12,16,7,277,2,110,105,101,295,121,116,331,355,347,352,377,372,342,337,362,366,74,69,289,54,59,209,214,189,194,199,134,139,129,149,154,64,204,144,89,94,99,294,79,84,327,328,329,324,325,326,249,254,259,264,269,274,229,219,224,244,234,239,179,184,174,164,169,159,34,39,29,284,49,44,24,14,18,9,279,4,114,109,104,299,124,119,334,359,349,354,379,374,344,338,364,369,71,66,285,51,55,205,211,186,191,196,130,135,126,146,150,60,200,141,85,90,96,291,75,80,300,302,301,304,305,303,246,251,256,260,265,270,225,215,220,241,231,236,176,180,171,161,165,155,30,35,26,280,46,41,20,10,15,6,275,1,111,106,100,296,120,115,330,356,345,351,375,371,340,335,361,365,73,68,288,53,58,208,213,188,193,198,133,138,128,148,153,63,203,143,88,93,98,293,78,83,311,309,310,308,306,307,248,253,258,263,268,273,228,218,223,243,233,238,178,183,173,163,168,158,33,38,28,283,48,43,23,13,17,8,278,3,113,108,103,298,123,118,333,358,348,353,378,373,343,339,363,368 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 = {74} 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 23:47:26 · history