Equation 677 Database

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Magma dc0a7d10da8b…

magma dc0a7d10da8b
Size
381
Isomorphism class hash
dc0a7d10da8b2240ec3db52653f666b8df37ae73107df38e39b713b46a4e406b
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 23:20:18
Display reorder
380,294,271,240,258,284,276,327,253,266,248,295,247,272,242,259,282,277,324,254,264,296,246,270,241,260,283,278,329,256,265,275,297,312,257,268,251,261,286,279,244,273,298,245,313,255,269,249,262,287,280,299,274,243,314,252,267,250,263,285,281,292,293,290,288,289,291,344,377,334,365,354,367,343,364,353,366,16,3,20,29,11,7,322,25,2,21,17,22,4,18,27,9,8,323,26,1,15,23,5,19,28,10,6,321,24,0,55,37,320,46,51,42,50,32,59,41,56,38,39,325,47,52,43,48,30,57,36,54,40,326,45,53,44,49,31,58,35,33,13,14,12,34,348,335,375,360,357,349,358,356,347,359,149,167,150,159,175,171,319,158,163,154,147,155,165,151,160,176,172,317,156,164,148,153,166,152,161,174,173,318,157,162,146,128,316,137,142,133,138,120,170,129,144,126,130,315,135,143,134,139,121,168,127,145,131,328,136,141,132,140,122,169,123,124,177,178,179,125,355,342,368,345,370,369,374,363,341,346,219,237,223,232,214,210,305,228,236,227,220,225,238,224,233,215,211,303,229,234,221,226,239,222,231,213,212,304,230,235,188,198,302,207,184,206,180,193,189,202,186,199,203,301,208,185,204,181,194,190,200,187,201,300,209,183,205,182,192,191,196,197,216,217,218,195,376,361,336,378,351,379,337,371,350,372,104,94,108,89,99,95,308,117,119,112,105,110,92,109,90,100,96,306,113,91,106,111,93,107,88,98,97,307,118,60,73,86,311,114,72,65,68,81,77,61,74,87,62,309,115,70,66,69,79,78,85,75,63,310,116,71,64,67,80,76,84,82,101,102,103,83,331,330,373,332,333,339,340,338,362,352 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#2570115b07c414cfeeb7a2c6e109688ea10588036adc8542cf84a052a83df0ff, 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 23:20:19 · history