Equation 677 Database

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Magma 19456f6c2351…

magma 19456f6c2351
Size
381
Isomorphism class hash
19456f6c235195c0396bfbc1d719306a16fd4bf162aaa366a28f12ca868e97d7
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 23:42:58
Display reorder
380,166,296,171,160,150,155,57,52,277,72,62,67,0,5,10,16,266,23,132,137,127,147,292,142,228,233,223,213,218,208,200,192,195,186,175,183,107,112,102,287,122,117,282,82,77,92,97,87,258,263,253,241,245,236,316,314,313,320,322,319,47,272,42,31,36,27,362,352,342,337,333,366,347,357,373,376,165,295,170,161,151,156,58,51,275,73,63,68,2,6,12,17,268,21,131,136,125,145,291,140,225,230,220,212,216,205,201,191,196,187,178,182,105,110,101,285,121,116,281,80,75,91,95,86,256,261,251,242,247,238,307,306,308,309,310,311,45,271,40,30,35,25,361,351,341,336,331,365,345,355,370,379,167,297,172,162,152,157,56,54,279,71,60,66,4,9,14,18,269,24,134,139,129,149,294,144,229,234,224,214,219,209,202,190,197,185,177,180,109,114,104,289,124,119,284,84,79,94,99,89,259,264,254,244,249,239,300,301,302,303,304,305,49,274,44,34,39,29,364,354,344,339,334,367,349,359,374,375,169,299,174,164,154,159,55,53,278,70,61,65,3,8,13,15,265,20,133,138,128,148,293,143,227,232,222,211,217,206,204,194,199,189,176,181,108,113,103,288,123,118,283,83,78,93,98,88,255,260,250,243,248,237,321,318,323,312,315,317,48,273,43,32,37,28,363,353,343,338,330,369,348,358,372,378,168,298,173,163,153,158,59,50,276,74,64,69,1,7,11,19,267,22,130,135,126,146,290,141,226,231,221,210,215,207,203,193,198,188,179,184,106,111,100,286,120,115,280,81,76,90,96,85,257,262,252,240,246,235,329,328,327,325,326,324,46,270,41,33,38,26,360,350,340,335,332,368,346,356,371,377 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {71} 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 23:42:59 · history