Equation 677 Database

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Magma 510820362bc8…

magma 510820362bc8
Size
381
Isomorphism class hash
510820362bc8e6cae67cfb1ab10c2b6b8e8244d4eef91332d9d57d3af70c3a24
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 23:20:52
Display reorder
380,136,96,176,216,256,296,315,316,317,312,313,314,61,101,140,180,220,260,184,224,264,64,104,144,45,46,47,42,43,44,284,84,124,164,204,244,297,97,137,177,217,257,265,65,105,145,185,225,181,221,261,60,100,141,41,36,37,38,39,40,285,85,125,165,205,245,335,332,331,338,342,341,371,360,372,367,120,80,160,200,240,280,301,300,302,303,304,305,95,135,175,215,255,295,191,231,271,71,111,151,7,8,9,10,11,6,288,88,128,168,208,248,281,81,121,161,201,241,270,70,110,150,190,230,214,254,294,94,134,174,3,4,5,1,0,2,289,89,129,169,209,249,337,336,356,366,348,347,376,362,370,357,103,63,143,183,223,263,326,327,328,329,324,325,86,126,166,206,246,286,196,236,276,76,116,156,52,53,48,49,50,51,293,93,133,173,213,253,262,62,102,142,182,222,277,77,117,157,197,237,207,247,287,87,127,167,56,57,58,59,54,55,292,92,132,172,212,252,365,361,340,330,354,353,378,334,379,339,109,69,149,189,229,269,307,308,309,310,311,306,91,131,171,211,251,291,192,232,272,72,112,152,28,29,24,25,26,27,282,82,122,162,202,242,268,68,108,148,188,228,273,73,113,153,193,233,210,250,290,90,130,170,32,33,34,35,30,31,283,83,123,163,203,243,358,363,346,364,350,349,373,359,375,345,139,99,179,219,259,299,321,322,323,318,319,320,74,114,154,194,234,274,199,239,279,79,119,159,13,14,15,16,17,12,266,66,106,146,186,226,298,98,138,178,218,258,278,78,118,158,198,238,195,235,275,75,115,155,23,18,19,20,21,22,267,67,107,147,187,227,343,352,369,351,333,355,377,344,374,368 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {70} 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 23:20:52 · history