Equation 677 Database

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Magma 9ccf8fc5c187…

magma 9ccf8fc5c187
Size
381
Isomorphism class hash
9ccf8fc5c1870901d69eb9fae6ad86e870ea696d4675e1e8d6d53fa41a756846
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 23:38:10
Display reorder
380,161,167,179,140,130,122,305,173,155,148,156,162,174,141,131,123,301,168,150,149,157,163,175,142,126,124,310,169,151,144,158,164,176,127,125,313,170,152,145,143,159,165,177,138,128,120,316,171,153,146,160,166,178,139,129,121,304,172,154,147,133,135,136,137,132,134,378,360,361,359,373,339,340,374,358,362,286,292,273,254,244,267,325,298,277,262,287,293,274,255,245,268,327,299,278,263,282,288,275,256,240,269,328,294,279,258,283,289,270,241,264,319,295,281,259,257,284,290,271,252,242,265,320,296,276,260,285,291,272,253,243,266,323,297,280,261,247,249,250,251,246,248,334,369,370,333,367,351,353,368,352,354,68,76,86,106,93,116,302,81,63,111,69,77,87,107,94,117,303,82,64,112,70,72,88,102,95,118,309,83,65,113,71,73,89,90,119,312,78,60,108,103,66,74,84,104,91,114,315,79,61,109,67,75,85,105,92,115,300,80,62,110,96,98,99,100,101,97,355,371,356,338,336,372,377,357,337,335,0,7,19,40,58,50,326,13,25,45,2,8,20,41,59,51,329,14,26,46,3,9,21,36,54,52,318,15,27,47,4,10,22,55,53,321,16,28,42,37,5,11,23,38,56,48,322,17,29,43,1,6,18,39,57,49,324,12,24,44,30,32,33,34,35,31,346,347,331,332,349,365,330,366,350,348,197,203,185,228,216,210,307,209,191,234,192,198,180,229,217,211,308,204,186,235,193,199,181,230,218,212,306,205,187,236,194,200,182,219,213,311,206,188,237,231,195,201,183,232,220,214,314,207,189,238,196,202,184,233,221,215,317,208,190,239,226,222,223,224,225,227,343,342,363,364,345,344,375,379,376,341 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#a2d5cf5003dd84c3a903146e7a6e34fbb5c6b0b2b4ddc575a055f83bab0bfd65, 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 23:38:11 · history