Equation 677 Database

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Magma d448258db089…

magma d448258db089
Size
381
Isomorphism class hash
d448258db089aec2774b3b6c3a3cd71cec5f258d0deec9c526b11e4c103dd3aa
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 23:33:53
Display reorder
380,236,235,233,234,1,239,69,70,65,66,67,68,37,38,39,40,35,36,71,72,73,74,75,76,167,168,169,170,171,172,299,272,277,282,287,292,229,230,231,232,227,228,319,320,321,322,323,318,161,162,163,164,165,166,247,252,257,262,267,242,34,33,29,30,31,32,337,338,359,371,367,368,358,377,343,342,219,218,237,215,216,217,120,121,122,123,124,119,96,97,98,99,100,95,118,113,114,115,116,117,110,111,112,107,108,109,298,274,279,284,289,294,214,209,210,211,212,213,308,309,310,311,306,307,105,106,101,102,103,104,249,254,259,264,269,244,89,94,90,91,92,93,347,346,348,373,365,366,349,379,351,350,149,154,150,151,152,153,189,190,185,186,187,188,7,8,9,10,11,12,191,192,193,194,195,196,26,27,28,238,220,25,296,270,275,280,285,291,160,155,156,157,158,159,328,329,324,325,326,327,225,226,221,222,223,224,245,250,255,260,265,241,3,2,4,5,6,0,334,335,336,370,356,357,332,375,362,333,140,139,141,142,137,138,131,132,133,134,135,136,52,47,48,49,50,51,128,129,130,125,126,127,15,16,17,18,13,14,297,273,278,283,288,293,144,145,146,147,148,143,314,315,316,317,312,313,20,21,22,23,24,19,248,253,258,263,268,243,44,43,45,46,41,42,339,340,330,372,355,354,331,378,352,353,80,79,81,82,77,78,60,61,62,63,64,59,202,197,198,199,200,201,58,53,54,55,56,57,173,174,175,176,177,178,295,271,276,281,286,290,84,85,86,87,88,83,305,301,300,302,303,304,181,182,183,184,179,180,246,251,256,261,266,240,204,203,205,206,207,208,363,364,361,374,345,344,360,376,341,369 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {71} 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 23:33:53 · history