Equation 677 Database

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Magma 775d4d53ed86…

magma 775d4d53ed86
Size
381
Isomorphism class hash
775d4d53ed868dcf8575afc960e3bfcca6a73c5d21087ed26f739c310a395d31
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 23:23:34
Display reorder
380,231,327,189,210,196,204,238,224,203,182,183,232,329,190,211,197,205,239,225,198,184,233,318,191,212,192,206,234,226,199,185,228,321,186,213,193,207,235,227,200,229,180,322,187,214,194,208,236,222,201,325,181,230,188,215,195,209,237,223,202,216,218,219,220,221,217,370,352,353,355,333,354,372,356,369,371,31,320,18,45,25,10,38,59,3,17,12,32,323,19,46,26,11,39,54,4,13,33,324,20,47,27,6,40,55,5,14,34,326,21,42,28,7,41,56,1,35,15,328,22,43,29,8,36,57,0,319,16,30,23,44,24,9,37,58,2,51,53,48,49,50,52,367,347,350,368,331,351,349,348,330,332,134,305,161,148,162,176,141,127,169,154,155,135,304,156,149,163,177,142,128,170,150,136,302,157,144,164,178,143,129,171,151,137,301,158,145,165,179,138,130,172,132,152,303,159,146,166,174,139,131,173,300,153,133,160,147,167,175,140,126,168,125,121,122,123,124,120,342,343,375,361,374,377,360,340,341,362,116,308,74,101,81,60,94,109,88,67,68,117,309,75,96,82,61,95,110,89,69,118,310,76,97,83,62,90,111,84,70,119,311,77,98,78,63,91,112,85,114,71,306,72,99,79,64,92,113,86,307,66,115,73,100,80,65,93,108,87,107,103,104,105,106,102,365,379,363,378,366,376,345,344,364,346,269,313,288,247,296,276,241,261,274,286,287,264,314,289,246,297,277,244,262,275,282,265,315,290,248,298,278,242,263,270,283,266,316,291,249,299,279,240,258,271,267,284,317,292,250,294,280,243,259,272,312,285,268,293,251,295,281,245,260,273,253,254,255,256,257,252,339,337,357,334,359,373,336,335,338,358 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#4a1fb8605639da49106a26631019a15cd198a6c8d9ed882322a7a649a8f8265a, 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 23:23:35 · history