Equation 677 Database

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Magma 9a0c3272b9dc…

magma 9a0c3272b9dc
Size
381
Isomorphism class hash
9a0c3272b9dc38de3bf07a71dc4de1839b0e8e60180f7eb3cf15488e006cf890
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 23:39:47
Display reorder
380,176,171,166,155,160,150,297,280,286,276,266,272,30,31,29,33,225,32,315,316,317,312,313,314,216,53,2,10,8,9,141,146,136,125,132,122,205,195,200,191,182,187,41,290,42,231,39,40,54,55,56,57,58,220,237,247,242,262,257,252,7,211,6,4,5,3,356,366,350,379,345,336,341,361,330,371,177,172,167,157,162,152,298,282,288,278,268,273,95,96,94,98,228,97,310,311,309,307,308,306,218,88,89,87,86,90,142,147,137,127,130,123,209,199,204,194,184,189,101,293,100,233,99,102,1,0,93,91,92,223,238,248,243,263,258,253,85,214,84,82,83,81,358,367,353,377,348,339,343,362,334,372,175,170,165,156,161,151,296,281,287,277,267,271,59,60,63,62,227,61,305,303,304,302,301,300,215,51,52,50,48,49,140,145,135,126,134,121,207,197,202,192,180,185,67,292,66,232,65,64,22,23,21,19,20,221,235,245,241,261,256,251,47,212,46,44,45,43,357,365,352,376,346,337,340,360,332,370,179,174,169,159,164,154,299,284,289,279,269,274,112,113,111,115,229,114,323,321,322,320,318,319,219,105,106,104,103,107,144,149,139,129,133,124,206,196,201,190,181,186,118,294,117,234,116,119,16,15,110,108,109,224,239,249,244,264,259,254,27,210,28,26,24,25,359,369,354,378,349,335,344,364,331,374,178,173,168,158,163,153,295,283,285,275,265,270,14,34,13,12,226,11,327,328,329,324,325,326,217,75,76,74,73,77,143,148,138,128,131,120,208,198,203,193,183,188,36,291,35,230,37,38,17,18,80,78,79,222,236,246,240,260,255,250,72,213,71,69,70,68,355,368,351,375,347,338,342,363,333,373 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {73} 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 23:39:48 · history