Equation 677 Database

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Magma eb4f7b406df5…

magma eb4f7b406df5
Size
381
Isomorphism class hash
eb4f7b406df543298b8d59b15dba7152d3ebac6004efa061a2794ee86956da06
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 23:47:21
Display reorder
380,102,97,107,4,5,82,87,77,72,292,116,120,112,131,135,297,92,125,35,27,30,21,10,15,202,207,212,217,222,227,142,147,152,157,162,167,182,172,177,197,187,192,281,285,276,265,270,262,51,41,46,65,55,60,301,300,302,303,304,305,257,252,247,237,242,232,352,342,337,362,347,332,377,372,357,367,101,96,106,0,1,81,85,76,71,290,117,123,110,133,137,296,90,127,36,26,32,24,12,16,200,205,210,216,221,225,141,146,151,155,160,166,181,170,176,196,185,190,282,287,277,267,272,260,52,42,47,67,57,62,319,320,318,322,323,321,255,250,245,236,241,231,350,340,336,361,345,330,375,371,355,366,104,99,109,8,9,84,89,79,74,293,115,121,114,130,136,299,94,126,39,29,34,23,14,19,204,209,214,219,224,229,144,149,154,159,164,169,184,174,179,199,189,194,284,289,279,269,274,264,50,40,45,66,56,61,329,327,328,326,324,325,259,254,249,239,244,234,354,344,339,364,349,334,379,374,359,369,103,98,108,6,7,83,88,78,73,294,119,124,113,134,139,298,93,129,38,28,33,20,13,18,203,208,213,218,223,228,143,148,153,158,163,168,183,173,178,198,188,193,283,288,278,268,273,263,54,44,49,69,59,64,314,312,313,317,315,316,258,253,248,238,243,233,353,343,338,363,348,333,378,373,358,368,100,95,105,2,3,80,86,75,70,291,118,122,111,132,138,295,91,128,37,25,31,22,11,17,201,206,211,215,220,226,140,145,150,156,161,165,180,171,175,195,186,191,280,286,275,266,271,261,53,43,48,68,58,63,311,309,310,308,306,307,256,251,246,235,240,230,351,341,335,360,346,331,376,370,356,365 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 = {73} 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 23:47:22 · history