Equation 677 Database

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Magma 1c1c2f9232b6…

magma 1c1c2f9232b6
Size
381
Isomorphism class hash
1c1c2f9232b6d284880a3850facbec7c7cf565bdb895047c4a49d377c1711a4b
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 23:46:56
Display reorder
380,74,84,79,224,89,267,272,297,282,287,130,122,127,145,135,94,277,140,29,219,28,64,69,59,113,228,118,99,103,109,54,49,214,42,32,39,20,21,293,3,2,233,197,201,206,182,187,192,156,161,151,171,176,166,248,238,243,263,253,258,310,309,311,306,307,308,339,349,344,367,331,361,378,353,358,372,73,82,78,222,87,266,271,295,281,285,131,120,125,146,136,92,275,142,23,217,22,62,67,57,112,227,117,98,102,108,52,47,212,43,33,37,16,19,292,17,18,230,198,203,208,183,188,193,155,160,150,170,175,165,245,236,241,260,251,256,326,325,324,328,329,327,337,347,342,365,333,364,377,352,357,371,72,83,77,223,88,268,273,298,280,288,132,123,128,148,138,93,278,143,25,218,24,63,68,58,114,229,119,97,104,105,53,48,213,44,34,38,26,27,294,1,0,234,199,204,209,184,189,194,158,163,153,173,178,168,249,239,244,264,254,259,318,320,319,323,321,322,338,348,343,368,334,362,379,354,359,373,70,80,75,220,86,265,270,296,284,286,134,121,126,147,137,90,276,141,7,216,6,60,66,55,111,225,115,96,100,107,51,46,210,40,30,35,12,13,290,10,11,231,196,202,207,181,186,190,157,162,152,172,177,167,246,235,240,261,250,255,314,313,312,316,317,315,335,345,341,366,332,360,375,350,356,370,71,81,76,221,85,269,274,299,283,289,133,124,129,149,139,91,279,144,9,215,8,61,65,56,110,226,116,95,101,106,50,45,211,41,31,36,14,15,291,4,5,232,195,200,205,180,185,191,159,164,154,174,179,169,247,237,242,262,252,257,305,304,303,300,302,301,336,346,340,369,330,363,376,351,355,374 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 = {67} 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 23:46:57 · history