Equation 677 Database

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Magma 072cbf6491a8…

magma 072cbf6491a8
Size
381
Isomorphism class hash
072cbf6491a8ffb03b553f026bae80711b2f56c2f4730e7978a3871739a819a5
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 23:29:29
Display reorder
380,290,141,146,125,130,135,309,310,311,306,307,308,155,160,150,295,171,166,200,191,196,185,175,180,225,230,220,211,216,206,240,245,236,255,260,250,1,6,12,19,267,22,25,32,37,42,272,47,86,75,81,95,90,281,57,50,62,67,277,72,116,121,285,110,100,106,370,366,336,341,330,376,356,346,351,361,293,143,148,128,133,138,319,320,318,322,323,321,158,163,153,298,173,168,203,193,198,188,178,183,228,233,223,213,218,208,243,248,238,258,263,253,3,8,13,17,268,23,28,33,38,43,273,48,88,78,83,98,93,283,58,53,63,68,278,73,118,123,288,113,103,108,373,368,338,343,332,378,358,348,352,363,294,144,149,129,134,139,324,325,326,327,328,329,159,164,154,299,174,169,204,194,199,189,179,184,229,234,224,214,219,209,244,249,239,259,264,254,4,9,14,18,269,24,29,34,39,44,274,49,89,79,84,99,94,284,59,54,64,69,279,74,119,124,289,114,104,109,374,369,339,344,334,379,359,349,353,364,291,140,145,126,131,136,317,315,316,314,312,313,156,161,151,296,170,165,201,190,195,186,176,181,226,231,221,210,215,205,242,247,237,257,262,252,0,7,11,15,266,20,26,31,35,40,271,45,85,76,80,96,91,280,56,51,61,66,275,71,115,120,286,111,101,105,371,365,335,340,333,375,355,345,350,360,292,142,147,127,132,137,300,302,301,304,305,303,157,162,152,297,172,167,202,192,197,187,177,182,227,232,222,212,217,207,241,246,235,256,261,251,2,5,10,16,265,21,27,30,36,41,270,46,87,77,82,97,92,282,55,52,60,65,276,70,117,122,287,112,102,107,372,367,337,342,331,377,357,347,354,362 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {76} 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 23:29:29 · history