Equation 677 Database

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Magma 627424601961…

magma 627424601961
Size
381
Isomorphism class hash
6274246019617b3a92b92060542f179af7250363ea4e25fc2277d03fe2e2f1bc
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 23:35:01
Display reorder
380,2,295,3,145,136,141,170,176,166,155,160,151,260,266,257,245,251,83,78,283,74,63,69,329,327,328,326,324,325,212,217,222,225,230,288,93,88,103,108,98,11,16,21,26,30,197,202,207,181,185,190,42,275,37,51,56,45,111,116,290,125,130,236,240,271,120,330,340,336,366,355,375,348,360,353,371,1,296,0,146,135,140,171,175,165,156,161,150,261,267,256,247,252,84,79,284,70,64,65,303,304,305,301,300,302,210,215,221,229,234,289,94,89,104,109,99,12,17,22,29,32,195,200,206,180,186,191,44,279,39,54,59,49,114,119,294,129,134,239,242,272,124,334,344,339,369,359,379,349,361,354,370,8,299,9,149,139,144,174,179,169,159,164,154,263,269,259,249,254,80,75,280,71,60,66,308,306,307,311,309,310,214,219,224,228,233,286,90,85,101,105,96,14,19,23,28,34,199,204,209,184,189,194,43,278,38,53,58,48,113,118,293,128,133,238,244,274,123,333,343,338,368,358,378,346,364,351,373,6,298,7,148,138,143,173,178,168,158,163,153,262,268,258,248,253,81,76,281,72,61,67,319,320,318,322,323,321,213,218,223,227,232,287,92,87,102,107,97,13,18,24,27,33,198,203,208,183,188,193,40,277,35,52,57,47,112,117,292,127,132,237,243,273,122,332,342,337,367,357,377,345,363,352,372,5,297,4,147,137,142,172,177,167,157,162,152,264,265,255,246,250,82,77,282,73,62,68,316,317,315,313,314,312,211,216,220,226,231,285,91,86,100,106,95,10,15,20,25,31,196,201,205,182,187,192,41,276,36,50,55,46,110,115,291,126,131,235,241,270,121,331,341,335,365,356,376,347,362,350,374 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {75} 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 23:35:02 · history