Equation 677 Database

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Magma 2f468e7f4d93…

magma 2f468e7f4d93
Size
381
Isomorphism class hash
2f468e7f4d933fa943ffa1c5c198fa3a1be3788fdc4ae10e5d1c4752e986072d
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 23:50:17
Display reorder
380,10,3,46,328,54,17,39,32,18,25,11,26,4,47,319,55,12,40,33,19,5,27,6,42,321,56,13,41,34,20,28,1,7,43,323,57,14,36,35,21,29,0,8,44,324,58,15,37,30,22,24,2,9,45,326,59,16,38,31,23,52,48,49,50,51,53,358,373,371,341,342,360,359,361,362,372,234,233,212,320,226,183,205,198,190,197,235,192,228,213,322,227,184,206,199,191,229,193,236,214,325,222,185,207,200,186,194,230,237,215,327,223,180,208,201,187,195,231,238,210,329,224,181,209,202,188,196,232,239,211,318,225,182,204,203,189,218,220,221,216,217,219,370,338,352,351,336,335,339,369,350,337,125,176,161,301,169,126,154,147,133,140,120,141,177,156,300,170,127,155,148,134,178,142,121,157,302,171,128,150,149,135,143,179,122,158,303,172,129,151,144,136,138,174,123,159,304,173,130,152,145,137,139,175,124,160,305,168,131,153,146,132,167,163,164,165,166,162,363,374,344,345,379,376,343,365,375,364,247,242,285,315,295,257,277,275,259,267,248,268,243,286,312,296,252,278,270,260,244,269,251,287,317,297,253,279,271,261,264,245,250,282,316,298,254,280,272,262,265,241,249,283,313,299,255,281,273,263,266,240,246,284,314,294,256,276,274,258,292,288,289,290,291,293,356,355,340,377,346,353,357,378,366,354,77,70,113,307,63,78,106,99,85,92,72,93,71,108,308,64,79,107,100,86,66,94,73,109,309,65,80,102,101,87,95,67,74,110,310,60,81,103,96,88,90,68,75,111,311,61,82,104,97,89,91,69,76,112,306,62,83,105,98,84,119,115,116,117,118,114,347,367,331,334,349,332,348,368,333,330 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#f58a04628c4b32a3a47f1e9514cd8eddf616a7738b914b3b5e3d18424442b87b, 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 23:50:18 · history