Equation 677 Database

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Magma 41bafc3bb9d1…

magma 41bafc3bb9d1
Size
381
Isomorphism class hash
41bafc3bb9d1071e37e6b9ac3f21d26f2e3abf54229c42464ed8ee513c6b8f07
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 23:28:42
Display reorder
380,114,109,119,124,129,134,49,39,44,64,54,59,74,79,69,294,89,84,244,249,254,229,234,239,94,99,104,8,9,299,194,184,189,179,169,174,29,289,34,14,19,23,269,259,264,284,274,279,314,312,313,317,315,316,159,164,154,144,149,139,219,224,214,204,209,199,334,349,339,358,379,374,354,344,364,369,110,105,115,121,126,131,46,35,40,61,50,56,70,75,66,291,85,80,241,246,250,225,230,235,91,95,100,0,1,296,191,181,186,175,165,170,26,285,31,11,15,21,265,256,260,281,271,276,321,322,323,318,319,320,156,161,151,140,145,135,216,221,211,200,205,195,331,345,335,356,376,371,351,341,360,365,112,107,117,122,127,132,47,37,42,62,52,57,72,77,67,292,87,82,242,247,252,227,232,237,92,97,102,4,5,297,193,183,188,178,168,173,27,287,32,12,17,24,267,257,262,282,272,277,308,306,307,311,309,310,157,162,152,142,147,137,218,223,213,203,208,198,333,347,337,357,377,372,352,342,362,367,111,106,116,120,125,130,45,36,41,60,51,55,71,76,65,290,86,81,240,245,251,226,231,236,90,96,101,2,3,295,190,180,185,176,166,171,25,286,30,10,16,20,266,255,261,280,270,275,324,325,326,327,328,329,155,160,150,141,146,136,215,220,210,201,206,196,330,346,336,355,375,370,350,340,361,366,113,108,118,123,128,133,48,38,43,63,53,58,73,78,68,293,88,83,243,248,253,228,233,238,93,98,103,6,7,298,192,182,187,177,167,172,28,288,33,13,18,22,268,258,263,283,273,278,305,303,304,302,301,300,158,163,153,143,148,138,217,222,212,202,207,197,332,348,338,359,378,373,353,343,363,368 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {69} 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 23:28:43 · history